I think the issue of whether or not you are insured to do a treatment is a bit of a red herring. Insurance companies are there to make a profit on the basis of risk. If something is high risk or likely to result in high payouts, then they will not cover it (or they will do at a high price - and example is young people's motor insurance premiums!). They are not experts at what they insure, they simply look at risk data, which is why they refer you back to your training. Unfortunately, quality of training is very varied so may or may not cover what you need to know. Obviously any professional should be insured to do the treatments they do, although there is no legal requirement to do so.
What is important is that as professionals we have the knowledge to carry out treatments on the clients and your insurance company won't be able to answer that. Pregnancy is not an illness however, there are changes that occur to the body and complications that arise that would contraindicate various treatments (sorry, am a massage therapist so can't comment on beauty treatments). Something else to think about is that until a pregnancy is established things can go wrong which have nothing to do with the treatments being carried out, but for the pregnant client, this can be devestating and they will be looking to find reasons. I am trained to treat women in their first trimester (it's not often covered in pregnancy courses or it's seen as a 'grey area'), however, I will NOT treat women who have had IVF in the first trimester because of what they have gone through to get pregnant even though they are at no higher risk than any other pregnant client for whom things are proceeding normally.
Ultimately, the decision to treat a client should be based on a therapist's knowledge, training and experience, not on whether you will be insured or not.
PS - Hot stone massage is contraindicated during pregnancy.
