Sorry to hear about your Dad, but Parkinsons is not the end of the world - it just seems so sometimes.
I was diagnosed 13 years ago at the age of 43 and have been trying ever since to get physio as I believe it would really help. The trouble is there just isnt enough provision in many areas so I would suggest that you take whatever help is being offered.
Muscle stiffness is very common in Parkinsons and any advice and help with relieving this can do no harm.
Go for it, and good luck to your Dad.