I personally find a physio to be well worth the costs, since injuries can be devastating when on important trainees, doctors are no prevention but repair tools in this regard.
And concerning the third doctor not paying for himself.... this is an excellent site imho to find out the best amount of doctors to hire to cure specific injuries in time:
http://www.student.ru.nl/rvanaarle/injury.php?lng=nl
edit: pop-up warning though, for those without a pop-up killer.