Your context is not long enough for me to be sure, as the proper idiomatic expression is “frapper fort”. Moreover “Mais fallait-il vraiment taper si fort?” is questioning if the reaction is exaggerated or not, whereas your English translation states that it is and questions the necessity. The difference is subtle but your translation is assertive (I would say “péremptoire” in French), whereas it is finely-shaded in French. Maybe something like “Didn’t you overreact?” (as suggested by Stéphane Gimenez) is closer to the author’s feelings.

Taper fort isn’t really an idiom, it is a natural derivation from an abstract meaning of taper. Taper means to hit, as does frapper, but there are different nuances in these two words. Taper fort is “hit hard” (subject to nuances), “taper si fort” is “hit so hard”.

In the context of a speech, taper sur quelqu’un (or sometimes taper sur une idée) means to argue vehemently against a person (or sometimes an idea). It implies that the discourse was not only opposed to this person, but expounded on the opposition at some length, possibly with exaggeration. There is however no implication of violence, dishonesty or inappropriate speech.

Taper fort insists on the way the idea was conveyed, not just on the idea itself. The author of the passage you cite implicitly concedes that he agrees with the core issue (that the “plaintes sur la corruption …” are founded), but disagrees that the speaker should have been so vehement in their expression.

To expand a bit more on the context: the author is addressing the Italian people after Italian elections. The means of expression was the votes in the election. The author agrees with the Italians’ discontent but disapproves of the extent to which they voted against the parties who were in power.

Here taper takes on another meaning, which is to hit something precisely. For example, taper dans le mille means to hit a target dead center (in the small central circle that awards 1000 points). The Italians have “tapé sur” the traditional political parties — they reduced these parties’ power. Frapper sur would not work as it implies physical violence. (Frapper sur can also imply a physical act without violence, as in “frapper du poing sur la table” — hit the table with one’s fist to attract attention, often used metaphorically. But if a target is designated, frapper sur implies a physical act against the target.)