Wealthy people usually spend more---just because they are less price sensitive and care more about other metrics.

I'm not sure how everything 'costs less'?

You could say that wealthy people can substitute money for time. So they need to spend less eg working hours for each good consumed.

I think he's getting at the pair of boots theory.

https://en.m.wikipedia.org/wiki/Boots_theory

I wouldn't go as far to say "everything costs less" but it is pretty well that established that poverty is very expensive.

A couple of key examples:

Food deserts often mean that groceries are more expensive in poorer areas as opposed to neighboring rich ones. Additionally, bulk food is cheaper but requires having enough funds to buy more than your immediate needs.

It is generally cheaper to own your own home than to rent and low income people are going to pay higher interest on the same home loan.

It is always cheaper for rich people to borrow money than poor people and poor people are often forced into debt in situations where rich people can dip into savings. Having to pay interest on your rainy day debt is way more expensive than getting paid interest on your rainy day savings.

That last one is huge, and tends to compound across all kinds of other areas, increasing the effective price that poor people pay for almost everything.

In the most general sense, it is often feasible to spend more money up front to save money down the road. The amount of interest poor people have to pay to do this reduces or even totally wipes out any savings.

This is all pretty well documented and studied. It's part of the unfortunate feedback cycle at the bottom of the economic bracket that makes climbing back out harder the poorer you get.