Are you sleeping in a bed? I think just waiting doesn't work. If you've done the pre-stuff, and you sleep in a bed, it should work fine. Can you sleep in a bed before doing the setup for the DB questline?
This might be a problem with a mod, if you're using any?
There's no level requirement; as soon as you get the letter the quest should start. I checked the http://www.uesp.net/wiki/Skyrim:With_Friends_Like_These...and http://elderscrolls.wikia.com/wiki/With_Friends_Like_These...#Bugspages for the quest and they both mention the game freezing after you get the note but neither suggest any fixes. It's for a different bug (no letter from the courier) but UESP says that sleeping immediately after telling Aventus that Grelod is dead might cause the quest to start right away without needing the note. I don't know if it'll work but it's worth a shot if you have an older save.
If that doesn't work, the only thing I can think of is uninstall all of your Skyrim stuff and start over from scratch. I'm on PS3 with the legendary edition as well and I've never run into this problem.
Well, good luck with it. Glad Frost popped up, I know nothing about consoles.