H.W.
Lots of great advice here.Awesome to read this site and see so many thoughtful moms.
I go a pretty nonpunitive/no rewards route with the children in my life. Recently, one was passing through a phase such as the one your son appears to be experiencing. Most of the balderdash was competitive and was a response to another child joining care with us. The child who was telling stories was very obviously cementing their place in my esteem and I heard some great ones. Once this child even claimed their father had suddenly become a professional baseball player and was teammates with a now-retired famous player! Hilarious. Because I was feeling frisky that afternoon, I casually said "Oh, I'll have to ask mom about that." to which the child replied "I don't think she knows---but she's gonna be so impressed!"
It is what it is-- an attempt to boost their little egos and make themselves feel important. I often just give it a little "hmm.." and go on with my business, especially when the stories are harmless. If they are violent, I point out which actions are inappropriate and could really hurt other people's bodies or feelings. Kids use stories to experiment with being rude, doing gross things, and doing things outside the rules their families have set. I try not to judge the child in question or blame them, but calmly state the consequences of these actions in real life. This gives them a chance to learn some values (kindness, respect for others, etc.) without actually taking the risk of doing something hurtful.
I have made some boundaries on the storytelling, letting the kids know that it's fun to tell stories, even ones that sound like real life, but that when it comes to safety issues or someone getting hurt, we need to tell the truth so the grownups know how to fix whatever the problem is. This seems to have sunk in.
I did find that paying no mind to the outlandish claims and giving the kids play people and props for dramatic play helped them voice their fantasies. Although sometimes I did have to leave the room when all the dolls were "barfing on each other". Ha ha.
And yes, definitely call a hurtful action as you saw it. When we ask a child "Did you do that?" we give them another opportunity to lie. "Why did you do that?" or a flat-out statement "I don't like when you do that" eliminates the temptation for dishonesty. And at this age, once that door is opened, it's hard for a kid not to walk right in.
One more thing: I have found "How to Talk so Kids will Listen...And How to Listen So Kids Will Talk" to be a great tool for working with verbally communicative children. Your son is at a prime age where this book would really be helpful in keeping your relationship with your son mutually respectful and strong. This book changed how I felt about my job as a child care provider and I find the work far more rewarding. As a whole, we have much less conflict, and our time together is far more pleasant. My relationships with the children have thrived and the children feel heard, which is so very important.