Isn't a B1 visa for business purposes? This is what the US Government website says:
Generally, a citizen of a foreign country who wishes to enter the United States must first obtain a visa, either a nonimmigrant visa for temporary stay, or an immigrant visa for permanent residence. The "visitor" visa is a nonimmigrant visa for persons desiring to enter the United States temporarily for business (B-1) or for pleasure or medical treatment (B-2). As examples, if the purpose for your planned travel is to consult with business associates, travel for a scientific, educational, professional or business convention, or conference on specific dates, settle an estate, or negotiate a contract, then you would apply for a visitors visa. As additional examples, if the purpose of your planned travel is recreational in nature, including tourism, amusement, visits with friends or relatives, rest, medical treatment, and activities of a fraternal, social, or service nature, then you would apply for a vistors visa. The visa allows a foreign citizen, to travel to the United States port-of entry and request permission of the U.S. immigration inspector to enter the U.S.
If someone had a private certificate and wanted a commercial licence or instrument rating would they not be described as a student for the course of study they are undertaking? I can't see them being described as a businessman.
I agree this is all academic. If you want to come to the USA for training you had better have an M1 visa or you won't get past the first desk.
Regards,
Chopperpilot 47