Lordy, has this discussion tanked.
The long and short of it, Rooneg and others, is that just because a DM says they'll check their player's logsheets, doesn't mean they automatically and inevitably will disallow anything they don't immediately recognize. All they are saying is that the AL allows DMs that option if they feel that it is warranted, which is the key phrase.
If someone sat down at my table and said they had an uncerted Wand of BFG from a module or scenario or hardback that I wasn't familiar with, and I thought it could have a serious deleterious impact on the table, I'd ask him about it. If he can back up the claim with an explanation of what or where, etc., fine. On the other hand, if he hems and haws and says stuff like "Er, I got it from that... big.... evil... thing in that one dungeon," I'm going to be much more suspicious about the legitimacy of that item. Since it's impossible to verify such an item in an honor-only system, I either have to take him in his word, or make a judgement call based on my suspicions, which is allowed to AL judges. Maybe I feel under the circumstances it wouldn't make a difference one way or the other to the enjoyment of the table. Maybe, however, I feel it would seriously impact the fun had by folks at the table.
That's all that's being said. It's an open-world OP campaign based off of purely an honor system, with, in most cases, little to no means to objectively verify anything at your table if you weren't privy to it yourself. That sort of system has got advantages and disadvantages. Sometimes, you have to take the one alongside the other.