As to the first paragraph of your response, of course, that can happen. But really, there was some pretty passive aggressive stuff going on here. Laugh emojis to mock someone? There is a whole thread about just this issue being problematic. It is passive aggressive, and I'm calling it out. This indirect aggression has a deep historical basis in the UK, so it isn't surprising it happens, but it is unfortunate that people cannot be direct and honest with each other and sort it out.
I also notice (and I don't think you are doing this), that when some is bullied, people like to say...oh, well, you know, they didn't mean it that way, or your tone is inappropriate. Blame the victim. This sort of stuff is rife to keep people in their place. Again, there is a historical precedent for it here in the UK based on class and gender and race.
Yes, the PT might have gotten the date of birth wrong because the DD sees him (her choice), 10 minutes a term. The rest of what he said may be very accurate. The OP's DD may be underqualifed, she may be nice and hardwording. So, fix the problem. Go in and sort it out. DD can get in touch with the PT, and get it fixed, go see the PT personally, get another PT, go see the HOS, write the people that judge the application, get another reference. Lots of choices possible. Many, many people have suggested this.
As I said upthread, you can complain and post here, you can put up with it, you can go through official channels, or the DD can go to what she thinks is a better university. That's it.