I was able to watch the vid before it disappeared and it was rather short in that you didn't seem to get anything of the run up to the incident. As has been implied above, so long as the siren is in continuous use, then a cyclist has plenty of warning of the approach of an emergency vehicle - probably a lot more than somebody in a car with the radio blaring etc - and it's generally not hard to get right out of the way, even if others don't respond with the same consideration towards others. OTOH, cyclists don't routinely have mirrors so they can be surprised by the unannounced arrival of a vehicle relying on beacons. When driving, as a frequent mirror-checker, I often see the blue lights before I hear the siren and if there's another vehicle immediately behind me, pulling over often leads them to pull out to pass me. Now, you might think that even if they didn't appreciate that I was pulling over because there were a couple of fire engines coming, that they would check their mirrors before pulling out but rather than mirror-signal-manoeuvre it's sometimes manoeuvre-mirror-look of sheer horror.
Drivers of emergency vehicles are subject to the law on dangerous/careless driving like everybody else and neither blue beacons nor sirens create any dispensations: in these circumstance they merely are to indicate to others "the urgency of the purposes for which the vehicle is being used." (Rather quaintly, the con and use reg's refer to "any gong, bell, siren or two-tone horn." Memories Of "No hiding place" and Chief Superintendent Lockhart's black Wolseley zooming out of New Scotland Yard with the bell ringing.)
A vid like this doesn't always record the distances between a vehicle and the camera, but it didn't appear to me that the rider was put in danger by the ambulance, unless they were disorientated by the sound of the siren, and that's not said tongue-in-cheek.
I'd not suggest that this type of warning equipment is never misused, but it has to be taken at face value at the time and without over-reacting, others should give these vehicles as clear a run as possible.
And FWIW, I got the impression that the ambulance driver gave the rider an unnecessary blast on the motor horn, which didn't reflect well on them. IMO.