So. If I have a stressed ship, can I give it an action with Squad Leader? Or is that illegal?

You can, but it can't perform an action while it's stressed so it's a waste of the action by the ship with Squad Leader.

That may seem like a strange answer, but it's an important distinction, because it's not that you can't do it, you can... But in most cases it won't do you any good. Unless that ship happened to be Tycho or had some other way of performing an action when stressed.

I'm not sure that it doesn't say somewhere that even when you can't preform normal actions that you can preform free ones...

There are a few grey areas where you just go WTF

I'm not sure that it doesn't say somewhere that even when you can't preform normal actions that you can preform free ones...

In the Rules Reference, p.3, second dot point under "ACTIONS", you will find this:

A ship cannot perform actions, even free actions, while stressed.

I'm not sure that it doesn't say somewhere that even when you can't preform normal actions that you can preform free ones...

There are a few grey areas where you just go WTF

You're confusing it with when you have to skip your Perform Action step, that doesn't stop you from performing free actions later if you're able. Unless you're stressed, and then you can't perform ANY actions.