I associate "fibbing" with:
1. Children telling minor untruths to avoid getting into trouble
2. White lies (untruths told to make people feel better, like "No, that dress doesn't make you look fat" once they are already out wearing it)
3. Tall tales (fish stories)
None of these involve malicious deception, intent to defraud, etc. (Okay, #1 is intent to deceive, but nothing that bad really happens if he did eat a cookie before dinner.)
A: Jerry, you did great in your presentation. You didn't look nervous at all.
B: That's a big old fib, and you know it, but thanks anyway. Glad it's over.
A: Alice, you look great. Your haircut is great.
B: Oh, stop fibbing. I know she butchered it, but it's just hair and it will grow back.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.