This isn't correct.
Don't confuse the salary cap with the bottom line, which includes "cash over cap" -- the actual amount of money a team pays its players in any given year.
Just because a teams' cap is, say, $90M, that doesn't mean they are paying out exactly that amount. When you figure in bonuses, incentive clauses, etc, it is common for a team to disburse a payroll larger than the cap, which in all actuality is really just an accounting mechanism.
Teams like the Redskins, for instance, with plenty of available cash, can spend more "cash over cap" than a lower-income team. If they are willing to mortgage the future, like Snyder is wont to do, he can push that cash-over-cap into future years and never really have to pay the piper -- unless the CBA expires and all his bills come due. That is why the Redskins were going to have to cut half of their roster if the deal didn't get done.
Think of it like disposable income. If you're making enough to pay the bills, fine. But if you have more than you need, you can either pocket it (like Bill Bidwell) or "invest" like Dan Snyder.