My DS has hypertonia and hyper mobility. I had no idea when he was a baby and sleep training was smooth, he was sleeping independently by about 8 wks or so (there were of course the usual bumps along the road since that age). He wasn't diagnosed until he was 3yo which may be that it was just missed by everyone or may be that his hypertonia is less sever. I would say that gentle sleep training the BW way should not pose any risk of health at all but if they are concerned they should check with their health professional before beginning.
I would also add that any form of CC or CIO method is extremely harmful to any baby whether they have hypertonia or not.
My focus would be on the method of sleep training (gentle and respectful BW methods and/or Pantleys no-cry-sleep solution which works very well with BW methods - gradual weaning for the feed-to-sleep prop and to encourage independent sleep) rather than whether or not it is safe to sleep train. When you sleep train gently it is clear there is no harm to baby as you are right there with them throughout the process until LO has the confidence to go it alone, happily, knowing that mummy or daddy will return as soon as they are needed.
hope this helps