If the official inflation figures (which are used to calculate that equivalent amount) understate the real inflation, that has the side effect of mathematically makinh the official GDP figure larger (because inflation is used to deflate the nominal - in dollars - GDP to create the official one).

There absolutelly is a political interest in the official Inflation understating reality (because it lets politicians claim as GDP Growth something is just the mathematical result of that understating error in the inflation figures).

It neatly explains why inflation is so consistently understated that dollar amounts at spearated by over half a century points in time which those official inflation indices tell us are worth the same do not in fact buy the same (i.e. are not worth the same) by a massive distance.

Random errors in measuring inflation would be just as likely understate it as overstate it and would not result in this difference in worth of a dollar amount thats several hundreds % off from the worth of present day dollars as measure by what it can actually buy.