I think those stories are apocryphal Elegran.
I have been living in very Welsh-speaking N Wales for nearly 3 years and I have never encountered this, not once, not ever. Neither have I encountered any personal hostility from people who might have assumed I was not Welsh.
Sometimes people will continue a conversation in Cymraeg, of course, if they are in mid flow. What are they supposed to do - guess you don't understand and instantly switch to English so that can listen in to their conversation? (It's their first language for goodness sake. ) Or are they somehow able to guess by looking at you that you don't speak Cymraeg and therefore cannot possibly understand the awful things they are saying about you?
Strangely, it is hard to tell who speaks Cymraeg and who does not just by looking at them, or even by hearing them speak English. I know several people who are not from the UK e.g German, Dutch etc, who are fluent Welsh speakers.
Often people do quickly switch out of politeness e.g. 3 men in a steam room in a hotel spa, talking about rugby, instantly changing to English when I said "hi" as I entered. Positively courteous.