Whether it's "true" or not obviously depends on the point of view of "when in the transaction that the transfer of money ownership takes place", but I definitely agree with the parent comment.

The problem with your house analogy is that (a) there can be long time spans between when your employer pays you and when you buy stuff in your house, and (b) you presumably have complete control over everything you decide to purchase in your house. That's not really true in the real estate example, where everything is part of a single transaction to which only one party is bringing any actual money.

A better analogy would be social security taxes in the US. In the US, the fiction is that the employer pays for half of an employee's social security taxes, and the employee pays for the other half out of their paycheck deductions. But basically every economist considers this a work of fiction, and since the true cost of an employee is everything the employer needs to pay, they basically consider all the social security taxes as costs to the employer.

I think their view is that money is fungible, and ultimately factored into the price the buyer pays. The agents aren’t getting paid unless there’s a buyer, so everything in a real estate transaction (the commissions and the property) is paid for using the buyer’s liquid assets.

When I’ve been a seller I’d have been willing to lower the price in a slow market more, had commissions not been a factor. Instead I shelved the listing until the market improved because I reached the lowest price I was willing to close at. So in that sense, the buyer is definitely paying for that commission via inflated price.