Are we reading our propane tank wrong, or are we being overcharged?
Your gauge is certainly not reading pressure. 

The only thing pressure tells you is what temperature the propane is at (LPG is "liquified propane gas" and reflects the fact that propane is easily transported in bulk because it becomes a dense liquid rather than a gas a relatively low pressure. That pressure varies with temperature.)

So, there's probably a float in the tank reading the liquid level. Such things are not uncommonly in error - if you think about the shape of a typical buried LPG tank (a horizontal cylinder), there's a complex relationship between the distance the float travels and the percentage of the tank that is full, which is being "interpreted" by a mechanical linkage.

If you have a local authority in charge of weights and measures, they (probably) check on the metering of the supplier. You could inquire if they do and (if so) when the last test was, and what it showed.