Not really. For example, our cadets in ADL need to renew their medical at least once. There is a registered doctor in ADL that are licensed to issue HKCAD Class 1s.
In terms of the OP, my guess is that he/she put on the medical form after being successful at stage 1 that he wore glasses. Maybe CX wanted an intial test done in CA first with the results forwarded to HK before they bring him/her to HK for Stages 2/3.
The OP mentioned a contrast sensitivity test. Thats just a fancy way of saying a colour test right? Anyway like I said, any opticians do the full eye test so I cant really see the problem? Unless you live somewhere that only has one optician per 10'000 population.
P.s yes i see what you mean now. The intital HK CAD Class 1 needs to be issued in Hong Kong. But CX dont want him to do the Class 1 in CA. Just get some optical results first.