I don't know about this particular story, but Kaspersky is certainly has strong ties with FSB, FSO and other official structures. I don't mean that it's their main business model — developing anti-virus software pays well enough not to be some cover story — but they're definitely _friendly_ on a deep personal level. Kaspersky himself was educated in KGB school, worked in government structures and has a lot of connections (which he used, for example, with that shady story when his son was kidnapped).
Usually, in Moscow, there is a strong correlation between being a highly educated, well-paid IT professional and having a negative opinion about current Russian regime; but judging from my second-hand stories from friends and colleagues, guys at Kaspersky tend to be very patriotic and pro-government. So, while I don't think that Kaspersky lab was founded deliberately like some sort of cover. But they're the kind of people who would definitely help FSB with whatever they ask — not because of some secret court order, but happily, thinking that they are serving their country and doing a good thing.