I have never in my life heard of calling 'C' note an 'F'... What is the purpose of that? I mean, you can call it F but the rest of band still plays 'C'? Interesting concept but my head hurts just from thinking of it..
I will explain as clearly as possible: Many rock guitarists call their lowest string 'E' regardless of which pitch it is actually tuned to, because this is a well-accepted style of guitar notation that any guitar teacher might teach their student. For example if you buy a songbook of popular songs that has both piano and guitar chords, the guitar and piano might be notated in different keys, to account for the capo or alternate tuning on the guitar. Here is some professionally-notated sheet music for a famous song. Notice that the piano is notated in the key of C, but the guitar chords are notated in the key of A, because James Taylor put a capo at the 3rd fret for this one.
These guitarists aren't dummies, and they aren't breaking any rules. The miscommunication occurs when they try to use guitar-style notation to teach songs to non-guitarists. They may not be aware that capo or
scordatura notation might be totally unfamiliar to non-guitarists, and therefore they are expressing the correct musical ideas, but communicating them poorly by using the wrong type of notation. It would be like handing bass TAB to a tuba player, or something like that.
For whatever reason, early on in my musical education, I decided that "bass guitar is a guitar-family instrument" and I was going to learn to read guitar notation. After a bit of practice, I was able to figure out that, for example, when a guitarist says "chord progression E, A, B in B standard tuning" what they actually mean is concert-pitch B, E, F#. This is a skill I'll have for life, that lets me read from guitar songbooks and jam with guitarists of all backgrounds. I can do these "mental gymnastics" in real time, even with an unfamiliar song, and it will sound good; we are all playing in the same key.
At the end of the day, however, the most important musical skill is having a good ear. Being able to hear that you are in a different tuning or key than the rest of the band, and adjust a few frets up or down to compensate, is a really valuable skill. Doesn't matter if you call it B# or whatever, so long as the whole band sounds good.