I read this as meaning that people with influence can make a difference.

Me too. At first...

Before I posted my translation, I went over a bunch of examples with "influencing people". In all of them, "influencing" was used as a gerund. 🤔

Влияние на людей может что-то изменить.

Uly gave a second meaning. And that's true, too / either, because the sentence in question looks like an example of syntactic ambiguity. Kinda Влиятельные люди могут изменить ситуацию.

спасибо

ramix ramix, you can't use "either" instead of "too" or "also" in affermative sentences.