My opponent is neither incompetent, ignorant or trying to trick me. I am more than willing to accept your judgement on the issue at hand, because of my experience of you and your tendency to be a very dry, "only the facts, ma'am" sort. Let's say no more.
Single-ship TFs certainly do get targeted by aircraft, so your opponent is ignorant/misinformed/mistaken on that point.
My latest WiTP opponent believes this myth. Is this something that was in the ol' game that was changed with AE?
In WITP, IIRC single-ship TFs could be used to game the system in the opposite way. Carrier strikes (in particular, but LBA strikes too) did vary in size but not by enough and small or single-ship TFs got way more aircraft than was practical. IRL a mistake like that might happen what with confused sightings and all, but it was pretty near all the time. A change was made (still back in WITP) to basically assign smaller strike packages to smaller targets, and it seems to have worked very well.
In AE that is still the case. It's also true that single-ship TFs, especially smaller ships, are more difficult to pick up on search, (and I presume) more difficult to get a hard fix on for targeting, and more difficult for a strike to find once it's in the air. They DO get targeted and they DO get hit, but they also can get through. BTW I am not suggesting that, say, 10 x single-ship TFs in the same hex are as hard to spot and hit. I have no experience with that but my guess is that they would be much more prone to being found, targeted, and hit. I base that on the fact that ships in different TFs but in the same hex are often targeted together in the same air attack in AE.
For my own part, I use single-ship TFs sparingly in what I figure are realistic situations. "Realistic" obviously is going to vary with the situation, with more desperation increasing the realism. For example when trying to sneak some supplies into beleaguered troops, or even slip some troops out. Areas where there seems to be no threat - obviously. Scattering a convoy that can no longer be protected. I'm sure people can add to the list.
Some people use them as pickets (I do not mean attack magnets as mentioned above). That is historical and therefore certainly realistic. People do argue about the parameters of that realism (which ships, military vs civilian, what exact circumstances, etc.). I don't have those answers, but it's really up to the opponents anyway as part of the game is exploring decisions that might have been made IRL.