I'm sorry but its just not true.
http://www.yas.nhs.uk/Calling999/doc...0E-version.pdf
Category C patients have their ambulance cancelled. So I guess in a way we're both right, in that they will put you in the queue for an ambulance but that doesn't mean its going to get to you or that they have to respond, they can tell you that you aren't getting an ambulance. You still have no legal right to an ambulance.
I spoke to our paramedics yesterday because I wanted to check, they rarely if ever go to a dislocation, they have done it if they have other symptoms but otherwise the 999 call handler will ask them to get there via alternative means. Although you're correct in that an ambulance will originally be assigned even if its then cancelled. So the OPs story doesn't sound like the full story.
My only experience of 999 was I got a phone call from an on call GP during, I didn't even get told to go to ED. Mainly because it was related to mental health but still...
The funny thing is you'd actually be faster getting there by Taxi than ambulance in this scenario.