Popular hearsay.
From what I understand from the very few ED have actually made on this topic (Wags, Chizh)
Su-27SM - wasn't allowed, several years ago. (Note version "SM" so very modern)
Su-24M - wasn't allowed (Again modernised variant with sophisticated avionics, sensors and weapons)
MiG-29 - doable but a hassle and F-1X fighters seem like better $$$
Russian aircraft in general - complicated (have refused to be more specific than that) for a Russian company.
People also often say there was some law in 2011/2012 that made it so... No specific law is mentioned of course but this around the time Sergei Shoigu became the defense minister and introduced a number of anti-corruption measures.
To OP, yes there was a Su-32FN mock-up/prototype proposed which was a naval version with a tailhook.