I agree that this quote speaks against the idea that Lanfear burned out. On the other hand, I think it's unlikely that the Finn could still her, or that - if the Finn or someone else could still her - it would be different from burning out, if you are transmigrated.

Personally, I think that Lanfear was at least temporarily unable to channel or stunned, because of her fall through the melting doorway ter'angreal, holding an angreal with Moiraine, etc. . Otherwise I doubt that the Finn could hold her (Moiraine might still have been burned out, though). Eventually Lanfear was killed and transmigrated in a too small body, in which Lanfear's whole potential couldn't completely unfold. BS indicated that this is possible:
"Ability to Channel/Souls. I think this has all been reported, but he [BS] stated definitively that the ability to channel is tied to soul. He stated definitively that the spark was not tied to the soul but could be affected by a specific body (i.e., if you had the spark in one life, you could be reborn and just have the ability to learn.) He stated with 85% probability that strength in the Power was not tied to soul, meaning that if you were an uber-channeler in one body, you could be weak in the Power in your next body." [empasis mine]

I believe BS might have thought that Cyndane was "weak in the Power", because her body was that small compared to Lanfear's, but Maria convinced him that the drop wouldn't be that large.

Finally, Aginor died before he could actually burn out, IMO, which would fit with BS's quote.