I watched the debate and he did not say those words. What he said was that because of the influx of so many illegals there is a housing shortage. Supply and demand. The Federal government and many blue states are subsidizing the cost of rents for those illegals, so rents naturally go up. No one is suggesting, other than you, that illegals are “buying our houses”.
Not only that, but because of the Harris/Biden economy, the price of building homes, at least in my state, has gone from around $125-150 a square foot to around $250-300 a square foot. Another reason for the housing shortage.