Isn't the point of the donation or ad spend to influence in some way? 

No different than when some influencer gets thousands of people to call a senator or rep, or hammer them on Twitter. That's the point, to influence. 

I run newspapers for a living, and actively engage in lobbying the state legislature and city politics (no national) on issues that affect free speech, press, public notice and public record issues, etc..

The line however is a payment for a specific act. That's bribery and very much illegal.  A do or can't for instance say here is a million dollars, if you do this. Not legally at least.