I was afraid you were going to ask that, and it's kind of a complicated somewhat confusing answer, but I'll try.
No, it is not necessarily that they are lacking zooxanthellae as they come in beautiful colors such as grey, violet-brown, off-white or a greenish, with some having blue, purple, and even mauve tips.
Some will say it is a good beginner anemone in the hobby and that is rubbish because it is a difficult anemone to keep and should
only be attempted by the advanced hobbyist who has a lot of free time to care for it.
They are beautiful animals but can be difficult to care for. If the greenish tint is in the off-white one you are in good shape.
I never found anything in my studies as to why the 'whites' don't do as well as the tans but have not seen anyone in the hobby with an odd-white have success.
IME, a nice purple, tri-color BTA's tend to a tad easier other than a Condy Anemones (still needs good light) which is pretty aggressive, moves around the tank and can/will sting and inflict damage to other anemones, corals, and fishes of course. I actually kept a Condy tank once to study with my two meanest Maroons. They actually loved them. Arg. Maroons. haha
Anyway, hope this made some sense. I'll shut up as I can be known to ramble.