Outside of the moral implication, this doesn't even logically make sense.
People are already facing higher costs, if you pay them lower, they will not work for you, because you know, commuting to work at your place will eat into the budget.
The main fault in their reasoning is the belief that higher living costs necessarily results in more people getting into the labor market.
At some point the marginal benefit to a worker becomes zero or negative, where higher living costs can actually result in a reduction in the labor pool. Whether we are at that point though, is not known yet without more information about the localized economy.
If I'm reading his point correctly ... He's saying there _was_ an employment crunch, and companies were competing with each other for employees by raising wages. He supposes that an increase in gas prices means that people need more money, so there are more employee hours "to go around". Therefore, companies don't need to compete as much with each other to attract employees, so they can go back to not paying as much.
You either get it for high skill industries or farm labor, no other employment.
Rising CoL because of energy and inflation -> people need the jobs more badly -> more labor available -> reduce wages
And before anyone tries to score a few easy points building a strawman, I'm just explaining the logic. I'm not endorsing it or saying it's ethical.
Maybe out of habit or something?