Here's the response from Dr Berry. Definitely wisps of the lawyers
I am sorry you are caught in this situation, because I agree that this is excellent and important training especially for those pilots flying at higher altitudes. As you are aware, it is our policy that anyone taking the PROTE training must have at least an FAA 3rd Class Medical Certificate. This is not a change in policy, but maintaining a long standing policy. Let me emphasize that the PROTE is not entirely without risk. For this reason, we require a physical examination in which we are confidant of the quality. We train our AMEs every 3 years, and do surveillance audits of them almost as frequently. A BasicMed qualification is not equivalent to a 3rd Class Medical Certificate. We do not have any oversight of the physical examinations done as part of the BasicMed process. For this reason, and the potential for liability, we will continue our policy of requiring an FAA 3rd Class Medical Certificate at a minimum. If you are serious about getting this training, I recommend that you get a 3rd Class Medical Certificate, in addition to your BasicMed qualification, take the PROTE training, and let the Medical Certificate expire naturally.