Those lids allow air to get in, regardless of how well you snap them on. Turning the container on its top essentially seals off that access. At least that’s my guess. All I know for sure is that it really helps prolong the shelf life. It also helps that you don’t lick off the spoon and stick it back in the container (glares at Ms. Chef).
Well, now that I look online, it would appear that this is an old wives’ tale. sigh…
I hadn’t come across this ‘wisdom’ about storing cottage cheese upside down, but your explanation seemed plausible to me. So now I’m interested. Which part is deemed to be spurious… that lids allow air in, or that the upside down manoeuvre makes any difference?