Why did the thieves guild believe Mercer Frey?

I love this game, and, even though I've moved to eso, I love the lore of the game. And now I'm wondering ... Why oh why did the guild believe Mercer Frey without even trying to find Karliieh to see if these "rumors" are true. But no. So anyone know why the guild was so utterly dumb?

Simply put, trusting him as the only remaining strong leader figure was considered the best choice for the guild's future at the time.

During the questline Mercer says: "Karliah destroyed everything this Guild stood for. She murdered my predecessor in cold blood and betrayed the Guild. After we discovered what she'd done, we spent months trying to track her down, but she just vanished."

They tried to track her down, but couldn't.

From her discussion with Mercer while you're paralyzed, it's clear she wanted to avoid open confrontation with Mercer due to his superior close combat skills, which is why she didn't directly go to the guild and, instead, tried to first capture him paralyzed, neutralize him as a threat.