I think that it is unlikely that Kaspersky has been able to elude the pressure from Putin and his friends given that their software is well entrenched in the US.
There's so little upside though. You do it once, and you're forever burned. Among actual security professionals, Kaspersky has a pretty good reputation - I'd ballpark their resistance to political pressure as better than most American firms' resistance to NSA/FBI/etc. pressure.
As far as I can tell, the worst-looking actors in this story are the Israelis, for hacking a private company, and the NSA employee who brought his tools home, if that wasn't a fabrication.