Yeah it seems good for characters starting at level 4, those starting at level 1 are too insignificant to have any juicy rumours, but early level events become rumour as you get further from the place, time and people involved
My group got to level 2 in a dungeon crawl in which they got pretty wealthy. They had a deal with the guy who owned the entry to the dungeon, which they honoured, but no one else knows what they faced underground, how wealthy they got…
I can imagine they’ll hear about their exploits amplified if they go to a t in a neighbouring town