I just wanted to add - someone asked if you'd use the hole in the ground, I wouldn't. LOL. Not unless it was an emergency. Not because I think it's gross though - but because I just CAN'T. Using those is like going potty outside while camping or whatever. I have never been able to get my clothes out of the way enough not to pee on them so I have to strip from the waist down!!
The trick with the method is to put all your clothes as close to your knees as possible if you're not wearing a skirt. Undies go right at the knees, and pant legs should be pulled up to your knees while the remainder of the trousers get bunched there, too. Obviously, if you wear undies without much stretch you can have some difficulty.
If you've got the privacy of a stall you can use one of those girl funnels at least part of the time. (Technically you could use one without the privacy, but I'm just imagining the tittering that you would hear all around you.) I've known a few older ladies who made funnels themselves out of butcher paper, because the commercially-available ones are expensive.
As for reversing the situation and asking how people in other countries would react, I think that for the most part they would just be pointing and snickering at you and making it a point to use a different sink. As long as they are strangers that's not so much of a problem, though of course one would try to only make a mistake like that once.
Another thing I think would make a difference is whether the person "mis-using" the facilties was an adult or a young child. A lot may be forgiven when it is a child; they sometimes catch you unprepared and you have to improvise, and most Moms know that this happens sometimes in a new environment.
To address the culture issue -- I think that any time you see someone make this kind of faux-pas, the first thing that you do is listen for a foreign language. Most of us try to be kind and give foreign visitors the benefit of the doubt in situations like these, something that we normally would not do if the person spoke unaccented English.
Plumbing quirks exist in every country, and the facilities in private homes often work differently than those in hotels and public buildings. Here's an example: One of the things that I always make a point to warn first-time US travelers to Ireland about are the toilets in private homes and small B&B's. They look very like US toilets, but the way that they are plumbed is sometimes very different. With older models, if you try to flush them more than once in quick succession you will stop them up VERY easily. Most of the time they need about 30 minutes between flushes to completely re-fill the water tank to full flushing strength. Many is the time I've seen a newly arrived guest couple apologetically approach the hostess and tell her that the toilet seems to be backed up. What happened is obvious if you know Irish plumbing; having just driven some distance they both urgently needed to use the toilet, but the toilet couldn't handle two uses in under 10 minutes's time, so it apparently got stopped up after the second use. The answer is not to rush to try to open it up, but to leave it alone for an hour or so, when it will probably flush just fine. (And the corollary tip to avoid the problem entirely, for multiple travellers, is if there is someone else with you who needs to use the facilities right after you do, try not to flush after the first use.)