Can you specify which stock craft(s) had this problem? I think I had a similar issue with custom crafts.
I started a new science mode and tried launching a simple Sputnik (I haven't tried the stock craft). I gave up after several attempts and re-designs because of the problem you mentioned, and I consider myself an experienced player. This would no doubt be frustrating to new players who try using the Stayputnik.
I think the issue in my case was drag at the top of the ship, where the radial size went from "tiny" to "small". Any small deflection would result in a large torque. The preferred orientation when falling was retrograde. If this was the issue, it makes sense that my manned crafts didn't have this problem. Fairings or an adapter would probably fix this, but they're unlocked much later in the tech tree. Slower ascent might also help. I had Aerodynamics quality set to "Low", which might play a role.