"He said, she said" has a sense that not only does an interaction look different from the two sides, but of an imbroglio.
There are a couple of moments I can think of that are "he said, she said" in the sense of two different experienced incidents for the two sides, but not in the sense of a nasty conflict where it is tangled to unravel what really went on.
My brother and sister-in-law have two little boys and the (nuclear) family is fortunate by having both sets of parents, two uncles, and one aunt within easy driving range. And sometimes, when the mother is at wit's end coping with the (perfectly age-appropriate) sort of behavior that inspired Mom's brownie recipe, their mother, or father if available, puts them in the car and takes them to a relative. And while the relative(s) in question try to be extra-gentle with the parent, the relative's perspective is (mostly) "Cool! We get to be with the little ones for an hour." There are no adult conflicts, and both parties have some idea of the other side's picture, but it is none the less two different views. One is—I hesitate to exactly say desperate, but a safety release valve for a difficult situation. To the other side it is more of a treat than anyone else.
Or for another example, there was one graduate program where I was the computer person for the department, and I was at a desk, not particularly stressed, when another student came in, looking not at all happy, and asked me to fix a printer so she could print out her thesis. I tried, briefly, to get it to print to the printer in question, and when that failed, I asked her, "Do you need it to specifically be this printer?" She paused; the thought simply had not occurred to her. She said, "No." I asked, "May I try to print it from the office printer?" She said, "Yes, it's on this USB key." I opened it up, started printing, and brought her the first few pages, and asked her if it was printing appropriately. This wasn't really because I saw as a live question whether the document was printing as she wanted; I wanted to reassure her. And I told her I would get the original printer dealt with on my own time, and opened a ticket at my next convenience. Now I haven't heard the whole story from her side (beyond saying that she was "apoplectic" when she asked me to help her), but I can take some obvious guesses that should be obvious to anyone who's been a graduate student submitting a thesis. I imagine that her version of the story started much earlier with trying to get a thesis ready before a some looming date, and she was thinking about how to revise and edit, wondering which wording was appropriate here and whether a section should be written differently there, and trying her best, and already we are at a very stressful situation. But after all that stress, she hit the "print" button, thought, "I can relax now, and it will print," and it didn't print, and nothing she could do or try seemed to change that. Under such conditions, tunnel vision is natural, and highly stressed people are much less likely to think of alternatives like "See if you can use another printer." She wasn't stupid by any stretch; she was quite bright, but just was acting like someone stressed out. (And I might comment that I was impressed by her manners. It's not terribly hard to be polite and agreeable when you are relaxed. It's impressive if you can be polite and agreeable when you are stressed to the hilt—and she was.)
Both of these situations are different on at least one point of a "he said, she said" situation in that all (adults) involved appreciate the other side at least somewhat, and that the two accounts can be connected in a coherent understanding. But there is nonetheless a situation that looks very different depending on whose eyes you are seeing it through.
Any closest words or expressions?