I should admit I was wrong. Covers in OG work, seems I got used to OXC and forgot how OG feels... Which is not surprising, considering i haven't played it for decades.
I repeated experiments once again, 100 shots for each, twice for OG. Well, "works as intended", and seems like the intention was to avoid OG behaviour altogether.
To clarify, this is the percentage of hits, blocked by cover, for similar battlefield state but for different game versions
Original game #1 — 55,6% - I call this "cover works"
Original game #2 — 57,1%
BAI / RA On — 36,8%
OXCE — 11,8% - and this is "doesn't work" to me
BAI / RA Off — 8,8% - ...this is my version in "OXCE mode", which is similar to OXCE at least in theory (doesn't work either)