This is a pretty blanket statement. That same down payment will not be effective at all. Current interest rates have definitely impacted housing prices but its not significant enough to make up for the difference in monthly payment. Think of it this way:

Scenario 0: 500k house, 30yr/3% interest rate, 100k down (20% standard) = 400k total loan amount and 1,686 monthly payment

Scenario 1: 400k house, 30yr/7% interest rate, 100k down (let's say you still have that cash and put it all towards down payment) = 300k total loan amount and 1,996 monthly payment.

This is assuming in your housing market prices have cooled by 20%, I'm not seeing drops like that in my market. Your monthly payment just increased $300.