It's important to remember that sarcoptic mange is difficult to diagnose even with a skin scrape it is not 100%. Many vets will choose to treat without a definitive diagnosis and see what happens. If it clears after treatment, which is fairly easy and not too expensive then there is your answer, if not then it is best to keep looking.
Of course I can't say that it is a mange problem, no one on the internet can, just letting you know that sometimes you don't get a diagnosis.
But as far as itchy cats and dogs go, mites are high on the list of possible answers.
Your vet should have done a skin scrape, if not you have the right to insist on one or get a second opinion.
Demodex is another possibility as has already been stated this mite lives in the hair follicles and it too requires a skin scrape to diagnose.
Sarcoptic Mange
Demodectic Mange
Good Luck, I hope your friend is much more comforatable soon.