This isn't true at all. They don't suddenly have more money to burn, and in fact, in the US, the amount you can borrow is based off of credit score, not the going interest rate.
I still don't really understand what you're trying to say to be honest. You owe the bank less at lower interest rates. Higher interest rates cause you to owe the bank more. You do not have to buy outside of your means if the interest rates are low, and in fact, the financially responsible thing to do is to buy well within your means while they're low and lock in lower interest for the term of the loan.
I think what you're trying to say is that when interest rates are low it becomes a seller's market. While true, this is not permanent and you will save money in the long run if you buy with lower rates. I think you're stuck on the short term and not thinking of the long term.
For example, rentals in my area have surpassed my mortgage payment by a good amount. If I didn't buy when rates were low, this: 1, may have not been the case due to higher monthly payments, and 2, I might have gotten trapped in the rental cycle and never been able to own a home, ending up paying more than what I would have if I purchased a home while rates were low.