Yeah I had read that a good number of anti-war people had gone there both before and after mobilisation. In fact I was watching a video by the youtuber "nfkrz" (from Chelyabinsk, left after the invasion and now lives in Tbilisi) who made a really interesting point. You can still travel to the EU if you're a Russian passport holder, however you do still need to get a visa from the destination country's embassy
inside Russia. So if you wanted no part in the war and made it across the border to Kazakhstan, Uzbekistan, Georgia or Armenia or wherever you are kinda stuck, you can't travel onwards to (say) Germany because that would mean
returning to Russia and risking trouble especially if you were supposed to be mobilised. Meanwhile if you remained (whether you were quietly against it, ambivalent or super pro-Z) you don't necessarily have that barrier[0]
Seems like a bit of a no-brainer to me - we should just allow Russians apply for EU/EEC country's visas outside Russia. If someone wants to not take part in a war, we should be making that easier for them as much as possible not harder or more dangerous :-/
[0] - I don't think it's easy but it's certainly a couple of levels easier than it is for those who left.