You mean the hydrogen accepting power(ie the negative charge) of the phosphates alone confers the name ‘acids’ to the molecules?
I had thought of it.. I wanted some confirmation.
According the Bronstead-Lowry acid/base theory, an acid donates a proton to solution and a base accepts it, not the other way around as you are saying. Phosphates are negatively charged because they have already dissociated to release H+ into solution.