I think you are dead on. The country needed a boost after combined results of 9/11 and the Tech crash. But they did too much for too long.
The interest rates were one step, but we also had “Liar Loans”, new Negative Amortization Loans, 100%+ loan to value loans. The market suddenly changed by bringing in thousands of previously unqualified buyers. And when the FED should have been raising rates, they were still cutting in June of 2003.
Prices are still sticky today in part because low interest teaser rates are still available along with Liar Loans.