Why do the Property Brothers consider the amount a buyer has for a reno as the approved loan amount less the purchase price of the house?

You have it all wrong. If you get approved for $500k, but buy a house for $400k

you will not receive $400k because you must have a down payment. Say you

have $50,000. for a down payment, then the bank will only loan you $350k.

Keep in mind that most parts of that program are not actual or even possible.

The buyers have actually already purchased the house and all the home

searching you view is just drama for the show. Don't try to rationalize it.

first of all, TV is not always like real life. second, the Property Brothers are Canadian and their show used to be filmed in Canada, where home financing seems to be totally different than in the US. Lately, more of their shows are done in the US but they don't delve into the financing aspect of buying a fixer in any detail. It's true that buying a fixer and doing major updating can save you money but in the US generally to buy a house and do major work on it you have to get a special type of mortgage if you don't have cash on hand to pay for the reno.

If you are approved for $500k then you have $500k to spend. You buy a house for $400k so the Property Brothers are correct. You have $100k left for reno.