It's not anyone, it's the police. It's not like a random stranger is asking you who you are. Being asked to give details by the police, and nothing more, is not something that should get anyones back up and I can't see why it does.
To be clear again, I'm not talking about being asked to stop taking pictures when you are within your right to do so. I'm talking about just being asked to prove who you are - to make sure there is nothing suspect going on, perfectly reasonable. And exactly what was going on in this story.
Same reason police do random checks of motorists to make sure they are the owner of the car and driving legally etc. You may be insured and driving your own car but that doesn't mean the guy at the lights next to you is...so would you rather just run the risk of having more illegal drivers on the road to smash in to you or have something done about it?
It's not like the police can just hold up signs saying 'if you are doing something bad please stop', so spot checks have to be done - it's for your own safety.