Hi Bally Heck,
Yes, I can confirm that a hydraulic failure constitutes a "Full Emergency" from the ATC point of view, even though it might not be a major concern for the pilot. As has been pointed out, hydraulic fluid leaking onto hot brakes is a possible fire hazard, and who is to say that the situation might not deteriorate by the loss of further systems? I speak from experience after being on the flight deck of a SSC in the 80s which lost one, then another of its three hydraulic systems completely unexpectedly.
Controllers are never criticised for "over reacting" to emergences; far better to be safe than sorry, after all, if things really went pear shaped we would look a bit silly if there were no emergency services in attendance. The bad
PR for the airline is not a consideration, I'm afraid.