Welcome to Joomla's world of quirks
Actually, at the expense of simplicity you get flexibly, which is either a boon or a pain in the backside depending on your point of view...
Now keep in mind that I haven't delved in to Flexicontent all that much yet, so I don't know much of what's different then stock Joomla. At least with com_content menu items (probably the same with flexi), as you pointed out you have a choice of displaying article title(s) AND/OR Page Title, which is really supposed to be for making a custom meta title. If you're on the front page or a blog view, the Page Title is turned on by default... thus you get the famous "Welcome to Front Page" with the dummy content. You can turn it off in the parameters or rename it (by default it is what your html meta title would otherwise be).
In css class speak (unless you override the core output because you want better/tableless output), stock Joomla uses the class contentheading for articles and componentheading for the page title (you won't even see H1 or H2 unless you have a decent template, are using a different content component like Flixicontent, or you use the Beez overrides or something). As for Emmanuals choice of doing it, I agree... but I usually modify it. I like article titles to be H1 on individual article pages, but h2 on blog/list views because for good SEO you should only have one h1 per page.
I'm still not quite sure if I've answered your main question. With stock Joomla It depends if you have a single article or a blog. In the article itself, if you turn off "show article title" (I don't think there's "page title there) it should work on a solo article, but not in a blog/list as the parameter in the menu item is then honored. My guess is that Flexicontent works in the same way, although I'm not 100%.