I can't imagine how it would be possible to detect a phone in close proximity without allowing this though

Accelerometer, by putting the two phones together and shaking (some app used to do this, but I can't find it with a quick search). Edit: I might have been thinking of Bump, mentioned downthread, though it's a different physical mechanism: https://en.wikipedia.org/wiki/Bump_(application)

Camera, and point it at their changing screen (or both at the same scene at the same moment). Not too intrusive.

GPS, but that would require location permission. Intrusive.

Audio, but that would require allowing microphone. Intrusive.

	▲	jaggederest an hour ago \| parent [-]
		slightly OT but the technology behind Bump was genuinely mindblowing at the time. Phones didn't have NFC or anything like that, and they didn't use much accuracy in the way of location data, so they basically just had a general "city block" location, timestamp, and accelerometer readings and would invert the accelerometer reading and look for identical accel + timestamp. We tested it one time with like 10 phones and everyone bumping each other / the wall as a control, in the same room and it nailed every actual pairing and ignored the others. The wiki has more, but lacks the subjective experience of how magic it was.