Shakespeare would have been able to afford a costume of this type
I think they are confusing painting with photography. I'm sure the painter could paint whatever clothes he wanted to.
I'm not an art historian, but...
There have been many known examples of statuary with interchangable heads, dating to antiquity, the most famous being the Chinese Terra Cotta army. Also, in the early days of photography, many photographers were known to create full-length portraits by taking the subject's head and adding it to a variety of stock body shots (I am vaguely aware of this being done in mid nineteenth century political campaign paraphenalia and would like more details).
Couldn't it be possible that some enterprising artist painted many copies of a young man's body and then painted various clients' heads on as a cheap substitute for a fuller painting?