What mistakes are you claiming are being made? The surveys measure what they're supposed to measure. That people have a misconstrued idea of what they should be measuring has nothing to do with the people reporting the information...
for their Public pay, government accountants could easily clarify what their statistics imply. (Un-)employment rates are valuable statistics, directly reflecting the current ratio of demand to, to supply of, labor.
And also, millions of Americans not currently, actively, offering to "supply" their labor, are not counted in those rates. Yet, many Americans assume (understandably) that they do. The natural assumption ("'unemployment' means everybody not working, right?") is
misleading, even when government accountants accurately calculate the statistics,
without manipulating numbers ("massaging the data"). Clarifying meanings would be beneficial, and not unreasonable to request & require, from Public-paid accountants.