n0, this is exactly what “indirect” elections are. Baalei batim direct their effort in certain direction and it indirectly affects Rabonim they do not control directly. Same, as a FCC or CDC chief may affect you iwth their decisions, but you have no _direct_ impact on their election, but do have indirect through all other elections you participated in.
This is not my idea, actually but a retort I got from a Talmid Chacham yearss ago. He was teaching about certain historical change in Ashkenazi teshuvos from business ethics towards pot-and-pan kashrus. So I asked what I thought was a sharp question – “so it is _your_ fault?”. He retorted – “No, it is _your_ fault”.