Somewhat guessing, but I think its more complicated than this - more like, if you went to look at how a dozen really great players do their thing, you might find at least several distinctly different technical approaches to how to use your fingers. Including the thumb, or not.
For example, two really great players, Eric Bouvelle and Domi Emorine playing
Sur les Ponts de Paris.) Notice also that they use only 3 of their five rows.
Now lets look at a Swede who doesnt come out of that school at all, but playing a nice French tune to stay with that theme, really great player Odd Arne Halaas plays
Sous le Ciel de Paris. All 5 rows, all 5 fingers, completely different technique.
So my theory is, the question should not really be so much A vs B or yes vs. no, whether you should use your thumb, but how you should use your thumb and fingers. (And the only real answer I have is not like I do it!)
[edit -- I should add, though - I dont use my thumb, and usually that means I really dont use it for anything. But it occurred to me recently that I miss a lot of notes during vigorous movement, and maybe if I used my thumb in that 3 row style, as a rest point ... and hello, that seems to help my hand stay in position better, as you might expect. The way Odd Arne Halaas plays looks easier, but his keyboard seems like it might be buttoned to his shirt, while Bouvelle and Emorine seem a little more loosely coupled to their accordions, maybe because they have a thumb free to rest on the keyboard. ]