So....not to defend her or anything but I could see assuming one didn't need a special visa for a short term visit that included some volunteering. Before I started using UK-Y, I might have made that same assumption. I also might have assumed that it would be ok to do work for a US company remotely while on a short visit in the UK/Europe. For the first trip, at least, I can give her the benefit of the doubt that it was an honest mistake. It's pretty easy to use google to figure out that you can visit for up to 6 months and it might not occur to her (or a lot of other people inexperienced in immigration issues) to research further for such a short trip.
But after that? When she gave up her apartment in LA and sold everything and moved over on a whim? Yea, she should have known better. If I read things right, she and Euan/Shaun/whatever didn't have anything romantically going on in person on the first trip and only "discovered" feelings after she left. So instead of taking another short-ish trip to explore that in person like a sane person would do, she just up and "moved." No wonder Euan/Shaun/whatever kind of freaked out.