When you're working with a bullshitter and can't just leave, what use is there in performative caring? Your coworkers may have still cared, privately, but actively complaining about it, presuming boss man doesn't care anyway, is just pissing into the wind. You may as well accept that he's a bullshitter and get over it. Some people are like that and it doesn't help you to spend your time seething over it.

If you can get him fired then go for it. Otherwise, you're only harming yourself by letting yourself dwell on it. As for believing him; when my coworker starts rambling about the time the Navy seals came to him for help, I just say "wow man, crazy". I don't believe him, but neither do I confront it. Why bother? I'm not being paid to call out his dumb lies. This is probably what your other coworkers were thinking.