If this is actually the cause (not saying it's not), then this is good information. However, as EL does nothing fancy (it's using the same mechanisms as docking ports), I know of nothing that I can do about it other than suggest avoiding clipping.
You say that the released vessel inherits this rotation. If the released vessel remains stable (off rails and without SAS) after killing the rotation (via SAS or going on rails), then for now at least, I suggest just being aware of the rotation (especially if it's predictable) and keeping it in mind the designs you launch from this particular station.
I have seen some weird rotations myself, all permanently canceled by killing the rotation one way or another (as mentioned above), but when undocking, not releasing from a pad (that I remember for certain; it may have happened, but not often enough to remember). However that station (or those stations, may have been more than one) have since stopped inducing such odd rotations, but they have been heavily modified since then: rather large chunks undocked and recycled (had some fun with this on one station, more later), and restructured to have some loops (via ReCoupler) to provided additional stability to my stations. All my releases (docking port or orbital doc) for the last while have been "rock solid stable" and the released vessel has drifted away as expected under micro-gravity.
As for that additional fun. I mentioned the issue earlier, but I have since discovered that it was not so much the shifts in mass (though I am unable to rule that out), but rather just PhysX joint instability, possibly coupled with SAS instability (again, more later): that particular station got exponential wobbles the moment I took it off rails unless I put a single auto-strut between a single part (a 5400u spherical tank full of scrap (so not quite as mass as one with LFO) and heaviest (nearby similar tank) or grandparent). KAS cable joints helped only briefly (one scene change). As I despise auto-struts, I create I experimented with a parts-loop (facilitated by compatibly sized parts and station hubs) to lock the offending tank with a second support. Worked like a charm
And now for unstable SAS: to understand this one, you probably need to understand l"linear systems and control" (this was the name of course I took (twice, flunked first time) in university for my engineering degree). SAS works well enough (its tuning is horrid) for single parts, or very small vessels when the extra parts just can't drag things around with their own momentum (every physical part in KSP has its own momentum, both linear and rotational, and they are all (within a single vessel) connected by springs, usually in a tree). This means that a simple vessel (eg command pod, chute, heat shield) will be nicely stable under SAS control (neglecting aero forces, of course), since the masses of the chute and heat shield are low enough compared to the command pod, and you have only the two springs (even more stable with just one or the other, but in such a vessel, getting the kerbal home becomes rather dubious).
Now, what happens when you start connecting comparable masses by springs? You get a finite element approximation of a tight string (or a singly supported beam (that support may be the center of mass, so even a free beam)). That is, tap anywhere and you get a wave propagating from that point to the ends, bouncing off (wave-guide stuff, btw), returning to the tap point (possibly at different times) passing through each other and repeating until damped out (assuming the spring connections have damping (friction)). This is a one dimensional. An easy two dimensional example is ripples in a small body of water where the ripples can bounce off walls cleanly (and is very good for seeing the mess you can get). Note that the tap can be linear (eg, RCS thruster, impact) or rotational (torque: reaction wheels or balanced offset thrusters). Place a control reference (just directional will do (and is all KSP provides), though a positional one results in the same) anywhere and a torque source (reaction wheels, RCS, doesn't matter) anywhere: you've now set up a feedback loop, with built-in delay lines (due to the wave propagation and reflection: this is why it doesn't matter where control reference and control actuation are placed). Introducing delay introduces non-linearity (if your vessel's behavior wasn't non-linear before, it is now), and there's no going back. Non-linear systems are notoriously hard to control, especially with linear control systems, such as SAS's PID (Proportional, Integral, Derivative) control. PID can control some non-linear systems, even those with delays, but only if that non-linearity (especially delay) is small enough, AND the PID is correctly tuned. If KSP does any auto-tuning of the PID, it is woefully inadequate (just look at trying to vessel with only four significant parts: it wobbles (as a whole) like jello), and I don't know where the knobs are for manual tuning (if there are any, stock). Get that delay (main source of non-linearity in KSP) too large, and all bets are off: SAS alone will shake your vessel to pieces, especially if that delay is "just wrong". If there is sufficient damping in the joints (dubious) or on the parts (aero), you might get some help.
The above is for PERFECT PhysX joints. That is, no floating point round-off, no integration errors, both of which are unattainable (former because it requires infinite precision: 24 bits doesn't get even close, latter because there's no analytic solution and numerical methods are required, thus integration errors). However, joint imperfections can be considered as micro impulses, thus can be damped (in theory), but will normally act as impulses to "tap" that slinky that is your station.
Finally, what I think was the cause my induced rotation after undocking: I suspect my station was busy vibrating like a violin string, but such that I couldn't see it (sufficient damping such that the oscillations never got out of control... exceptions above). Then, when docking (note, not undocking), the oscillations caused the two docking port colliders to intersect when KSP joined the two vessels together, but as the two vessels had become one, the "no same-vessel interaction" kicked in and removed that source of corrective force. The intersection would have been too small to be obvious, but sufficient that when the two vessels were decoupled, PhysX kicked in and forced the two colliders to no longer intersect, but because the intersection was small, the force was small and thus the induced spin on my ships was not overly dangerous. It was always such that it looked like an offset (from CoM) linear force: the undocked ship was pushed away from the docking port (at about 1m/s) and spun a bit (pitch and roll: mk2 inline docking port) indicating that the intersection somewhere either side of the ship's center-line and fore of the CoM: thus likely the docking port, just either side of it.
Thus, my only worthwhile suggestion is to ensure your station is stable. That is, oscillations (due to any cause) die out with SAS enabled or disabled. Struts, loops (recoupler), even auto-struts (despite my loathing for them, but they must be strategic) can (but might not) help by shifting your station's natural frequency somewhere less sensitive and thus poles (control theory stuff) to the negative half-plane.