But this isn't true, either: "but in S-Corp when you do not have enough cash to pay yourself paystub so you are not allowed to take distribution."

That's two different things you just tied together. The one does not preclude the other.

You can be running an S Corp which has loans and/or grants (ie hurting for ready cash), and they need to pay payroll to whoever is doing the work. Having enough cash isn't the definition; if they had cash and used it unwisely or to acquire assets or pay down debt, for instance, that's just bad management.

Now, is it a good idea for a business entity having debt to use the funds to give distributions or even bonuses to staff? Probably not, unless they also know they have contracts settling later, for instance. But that's exactly what some startups will do; go into debt to cover operating costs until they are up and running. Or, give a bonus to staff that wrote a grant request or landed a big loan.

It's not unusual for a flailing business to pay retention bonuses to hold on to some high performing staff, to keep everyone that could turn around the business from jumping ship prematurely. And plenty of times, a distribution is taken where it becomes taxable income to the shareholder, as opposed to paying out retained earnings (prior taxable income). It isn't advisable, but they still take it, "Because we were sitting on all that cash, anyway. Why shouldn't I take some home?" So, that's an example of them having cash, but it wasn't theirs to take personally.

Until you run into the variables of how all of this is intertwined, you might want to pull back from your definitive statements.