I don't think that is accurate.
Most post-doc are funded through soft money (i.e., grant money or other non-earmarked department money) to a principal investigator. The PI wrote the grant and budgeted for post docs. Meaning that they set the salary for the postdoc in advance at the time that they wrote the grant (most grant applications I was part of required approval from the University's finance office before submission). They can increase the postdoc salary if they want.
The problem is that if they pay more for a postdoc, that money will need to come out from something else and usually that's from other personnel expenses (as most funding agencies have set amounts that they will allocate to spending categories, so you cannot propose a grant with only personnel expenses for example). That means that increasing the postdoc pay will either (1) reduce the number of postdoc that can be hired on any specific grant or (2) reduce the amount of compensation that a PI will get from the grant. You can see how both of those option are a non-starter as (1) will reduce the manpower on the grant, leading to less productivity, and a reduction in likelihood of future funding and (2) is just a non-starter as most PIs feel like they should get something out from getting a grant (i.e., they don't do research just because is fun).
Plus, there is a close to infinite supply of recent PhDs in pretty much any field that cannot get a faculty position and that will apply for postdocs, so there is really no market incentive to increase base postdoc pay.
Note, I have only applied to NSF grants so other funding agencies (i.e., NIH) might have different budgetary requirements. Private foundations are the Wild West of funding and each one has its own requirements.