TBH, regardless of the NYT and their recent "red-scare", I'd be concerned with using them on sensitive systems -because either knowingly or unwittingly they could have FSB moles working for them.
I have no idea one way or the other (regarding either the NYT or Kaspersky). But it does strike me that your theory is credible.
However it also seems credible that Microsoft, Intel and other critical hardware and software vendors based in the US may have moles and/or agreements in place with CIA/NSA.
That's possible as well but if you are US based at least the damage is contained --the NSA isn't going to give your data to a foreign competitor (or local for you have recourse in the legal system), whereas I'm not so sure the FSB would not "share" information with their preferred firms and if you become aware of it, you would have very little recourse.
Unless you aren't in the US or Russia, then you have Russia potentially spying for Russian companies/government, and the US/NSA potentially spying for US companies/government. The NSA has been caught with their hand in the cookie jar when it comes to corporate espionage[0][1].
I think it's common knowledge industrial espionage is practiced from time to time by all major powers. The question is a calculus. Who'd put you in a smaller/bigger ditch, relatively speaking.
You really don't need FSB moles if the property and even personal survival of the CEO is in the hands of an authocratic regime.
No Russian citizen in Russia, especially not anyone with any kind of wealth, can deny the government's requests. Whether the influence on Kasperky is from the top or only starts further down the chain, is more of a stylistic aspect of handling intelligence assets...
This, too, is not unique to Russia. Joseph Nacchio was CEO of Qwest[1] when he refused to hand things over to the NSA. Lucrative government contracts were then dropped, Qwest's earnings took a hit, and Nacchio was subsequently prosecuted for insider trading. As I understand it, the accusation was that he knew they were not going to meet their earnings forecast and his contention is that he did not because the government contracts being dropped was a surprise to him.
"Since being freed in September 2013, Nacchio, 65, has repeatedly denied he engaged in insider trading, arguing that he thought Qwest had opportunities to get federal contracts that would have boosted its revenue, but those opportunities were withdrawn after the company's alleged refusal to cooperate with a National Security Agency surveillance program.
Nacchio has suggested repeatedly that the government's prosecution of him was payback for not helping the NSA."[2]
Even if it turns out that Nacchio really is guilty of insider trading and the government did nothing untoward, one can see how easy it would be for the US government to destroy the life of a CEO they find uncooperative.
That seems to be a rather particular case, of which the details are not publicly known. It could easily be that the NSA had a particularly good reason to withdraw the contracts, and obviously the company didn't have a right to these contracts in the first place, or the NSA wouldn't have been able to stop them.
On the other hand, the NSA is not controlled by the government, at least not to the level of individual prosecutions, investigations or contracts.
One can, and such an article would also be 100% correct. Even if Symantec doesn't partner with NSA today, there's certainly a potential for them to be doing that tomorrow.
The pragmatic difference is that it's very hard for another country to completely avoid relying on software products created in the sphere of influence of Western spy agencies, whereas it's relatively easy for US to ditch Kaspersky.