I think there could be something in this... but also low fat or full fat, it's not a great idea to add milk of different freshness dates to each other, its contaminating.
How is mixing up the milk considered part of cleaning anyway?
It's a shame that you feel that discussing this with management would make you feel ridiculous - it's an odd thing that she's doing, which affects your entitlement to milk, which presumably is one of your work benefits. You shouldn't be made, or let yourself feel, that it's so trivial its ridiculous. People are being urged every single day by doctors to cut their cholesterol - so it's not a small issue at all, especially since you got people to agree it was fine for you to have low fat milk.
If you don't feel you can discuss it with management, maybe talk to the people you canvassed in the first place. I bet they would agree it was annoying. In the meantime, I like the thermos idea, so at least you could be sure. I got so hacked off with the office tea/coffee issues (they had a contract for a disgusting dispensing machine) that I started having black tea/coffee or peppermint tea and once you do that, its like giving up sugar in drinks, you can't go back.
Also liked a pps suggestion to bring in all kinds of weird milks 😀