I think the therapist is subscribing to some outdated AP philosophies.
When (most mainstream) people nowadays talk about AP parenting and how it is based on outdated concepts, I believe they are referring to the philosophy that your therapist is espousing.
That philosphy is that, somewhat like a baby goose, the bonding and imprinting process happens during pregnancy and then shortly after birth and if anything interrupts it, the lifetime bond suffers.
Actually bonding of humans to their babies is MUCH more complex than that and is something that takes place over time. There are many things that are deterimental to bonding - pregnancy complications, lack of or inability to breastfeed, NICU time, birth complications, having the baby in a nursery instead of in the room, and so on. But since bonding is a complex and long-term process parents and babies are able to overcome many of these things.
I don't know the guy personally and maybe I just don't know what I'm talking about, but that seems to be the place he's coming from.
And, you are not her mother... but you seem to be a strong and positive female role model in her life. It seems to me (a totally ignorant person) that there is a big gray area, where on one end you are providing a somewhat emotionally distant role model, and on the other end you are acting as her mother. Honestly, I don't think any one person has the answer as to whether you are misguided by being involved to that extent. Probably only you and stepdaughter understand all of the complexities here.
My question for the therapist would be... does he feel that adoptive parents should also discourage their adopted children from calling them "mom" and "dad"? After all, they are a replacement and not the real thing, by his logic. So what's the difference? If he feels they should call them mom and dad, I don't see what the difference is in your situation, if biomom is truly not around. If he feels they should NOT call them mom and dad, then quite frankly I think he's full of crapola, personally.
Not sure if this helps any. Good luck mama.
You can only do the best you can do.