You don't need to know BFS, you need to show that you can come up with a BFS implementation if you need to do so. You can always say "wait, remind me again, which one was BFS?" and the interviewer can certainly tell you at least what the conditions are. Maybe he might think a bit less of you (although I personally wouldn't) because BFS is a really really common name in the jargon of a programmer, but still it's better than simply blanking out and then angrily claiming that it's unfair to ask BFS.

A similar question could be "Can you print in order all the elements of a given tree/graph?", would you find that more fair compared to straight out using the word "BFS/Breadth First Search"?

Because it's not intuitive to some people. Some people just don't 'get' it. The assumption is that such people are probably also not good software developers.