I am a lawyer. What I can tell you is that there is a lot of bad information and bad advice being given here. Not all of it is bad, but lots of it is bad.
I'm not going to give you advice, if for no other reason than that I'm not licensed to practice in Alaska and in any event I don't know how Alaska law might differ from California law.
What I can tell you is that based on my knowledge of general principles and of how lawsuits generally work, I can see why the shop owner might be concerned about you diving with customers. (Re-read Jax' post.) I don't know if the owner's concerns are warrant prohibiting you from diving with customers. But, I can sure see why it might worry the owner. And, it is more likely than not that the owner's requirement is within what the law allows. OTOH, if something goes wrong on a dive, the shop could end up getting sued even if the victim is not a customer of the
The bottom line here, as in most instances, is that the question is not whether the shop is likely to be found liable, but rather the cost of defending a lawsuit.