Fining, and even coarse filtration, leave yeast in the beer. Only very tight sterile filtration will remove all yeast. Beer that looks perfectly bright can still have many thousands of cells per milliliter, plenty to carbonate.
...can and probably should, but I wouldn't and won't bank on it. It really sucks when you wind up with a couple cases of flat beer that with proper carbonation would have been spectacular.
How did you know that was the problem?
Cuz the beer was flat and remained that way? Other than insufficient healthy yeast, I'm drawing a blank on what would cause primed, bottled beer to fail to carbonate.
To Dave's comment, IME also high gravity/high alcohol beers are always more challenging to bottle condition than lesser beers. I generally prime with saved wort from that brew, and ALWAYS inoculate it and verify active fermentation before pitching to the vessel and bottling. Most of the time I use harvested yeast from the same batch, but have also used CBC-1 quite a bit in the past. My experience is that harvested yeast is more reliable that rehydrating and pitching CBC-1. My process works reasonable well for everything except BIG & barrel aged beers, I bottled an IRIBA 4 weeks ago after 1 year in a barrel and it's just now up to ~1/2 to 1 volume of CO2. That one was OG 1.102 & FG 1.026 and it was primed with corn sugar. Another couple months and it might have enough carbonation to produce a week head