Sometimes I think a question like this is one of moral versus legal. The reality is that you know you owe the money because you received the services. You're right that the bill should have been sent to you, and the natural urge for many people is to just count it in the win column when things like this happen and there's the chance to avoid paying.
I suppose my question for you is, are you comfortable with the notion that you are not paying something that your heart of hearts tells you should be paid? If roles were reversed and you, as a business owner, had forgotten to bill something for which you were rightfully due payment, wouldn't you hope they'd have the integrity to pay you anyway?
The legal side of this can be a bit trickier, and much depends on the state you're in (assuming you're in the U.S.) because some have stiffer consumer collection and protection laws than others. The rehab center could, when doing an audit of its accounts, discover that you didn't pay for these. They could take the polite course of action and call you with a gentle reminder or send a bill, or they could be not so nice about it. Either way, they can't send anything to collections for which you haven't been presented a bill and demonstrated an unwillingness to pay. There's a process in place, regardless of the state, so they can't just automatically put it into collections.
I will close with this question for you: did the rehab center help you with what you needed, and are you healthier and better because of their care? If so, pay the bill. That's my advice. Keep in mind that unpaid medical costs just raise the prices for everyone else, because these providers will make up for the loss somewhere.
I hope this helps.