Oh gosh no, not the 'staying nearby' parent! Sorry OP, I agree you've taken differing views on board with good grace & humour, but honestly, unless there's a specific need it's just undermining.
My personal favourite of helicoptering taken to ludicrous extremes was on my dd's year 5 residential. One of the parents had a connection with the hotel. They arranged for one of the hotel staff to covertly photograph & video the group having breakfast, assembling to go out for the day, enjoying a quiz in the evening etc etc.
All the images & clips were posted on a parents' whatsapp group. Cue parents requesting shots of specific kids ('can you tell him to look out for ds, he's a tall boy with red hair... ', grumbling that ' well I don't think Mrs Thing needed to snap at those girls like that, they were only chatting! ' &, hilariously, ' my dd had her hand up first! This quiz is obviously rigged! '
As soon as a couple of us who are parents but also teach at the school were added to the group, we blew the whistle. BIG hoo-ha.
Now, I'm not suggesting for a minute OP that you're this kind of nuts just for being a bit anxious, but you can probably see why teachers occasionally get defensive in the general direction of hovering parents...
I think you should follow a PPs suggestion : meet the HT, explain that ds isn't keen but you want to keep the option open, & quietly pay the deposit. But if you know it's just going to be a 'nope', quick email saying he won't be going is fine. It's not compulsory.