My understanding is that a possible link is the FSB Certifications issued by the Russian government, to Kaspersky do not bear the stamps of just any company seeking to operate in Russia; starting in 2007, they also include a Military Intelligence Unit Number, suggesting a possible connection to ongoing FSB operations.
What that connection is and what, if any, active role Kaspersky (The company) has is another question. It may be that the FSB has to workaround the Kaspersky Security software and that is why there is an associated Unit Number.