In general terms police officers or PCSOs are not allowed to ride on the pavement. They are to be held accountable as anybody else. Vike's answer was that under certain circumstances he would be able to justify riding on the pavement after properly risk assessing it. In other words it would be justified to do so, as long as it was in the proper execution of his duty.
If you feel that strongly about it, then challenge the next one you see doing it. If they are able to give you a reasonable explanation, then accept it. If they can't, and you believe that the world will be a better place if you make a complaint, then you are perfectly entitled to do so. Posting a video on Youtube however is about as spineless as it gets. There's no opportunity to hear a reasoned explanation, you'll distort the truth by making assumptions and inviting criticism from those with opinions, but no knowledge of the facts.
On our patch there are many footways, ginnels, paths and off road cycleways. A cop or a PCSO on a bike may well have to use some of them in places simply to get around. They can visit places on their patch by the occasional shortcut. If they do, they have been told that if they inconvenience anyone or injure somebody in a situation where they could have been off and wheeling the bike, there is nothing that will get them out of the mire.
That said, in my opinion as a team leader who reguarly deploys cops and PCSOs on bikes, there can be no excuses or justification for sloppy riding, or setting a bad example. All of the riders have been told that, and I would have personally challenged the ones in the examples above who RLJ'd or pavement hopped.
Here's a little hypothetical quetion though. If your elderly mother had her purse stolen in the pedestrianised precinct, CCTV picked up a suspect and one of the team was despatched to catch the thief, would you be happy if they got within a few yards of the suspect, and then dismounted to walk the precinct so as not to annoy the likes of Thomas?
Common sense and reason is all that is required to think it through.