well I guess this whole page would need to be rewritten then https://www.galciv.wikia.com/wiki/Influence_starbase
Wikis are by definition ongoing projects, and it looks like that page had a "lead author" (Varis) who hasn't worked on it in quite a while.
The current wording indicates that no one who worked on the page had an authoritative source to answer the question about boosting other influence vs. just adding its own. (I'm not used to seeing question marks on wiki pages outside of quotations, but it seems better to do that than just guess and try to sound confident.)