I'm with Bettypooh on this one. If your friend asks why you were Googling what happened, just tell him that you wanted to see if anyone else had gone through a similar situation as your friend. (Obviously we know the answer, but he doesn't need to know that.)
Anyone suggesting that this just be swept under the rug is only contributing to the perpetual loop of what we've all had to suffer through when there's no reason to continue it. If this kid has taken diapers in the past on several occasions, he definitely has DL tendencies, and will likely be a closet DL who spends a good portion of his life ashamed of himself, and who inevitably winds up sneaking onto sites like this as a teenager lurker in a few years, while hopefully being one of the people who registers and joins that really long list of "guest members" who aren't supposed to be here. The sooner parents realize what they're dealing with, the sooner we can put an end to the closet DLs and this wheel of shame that comes with them.
I know I'd never want to be in the situation that you were in Diaperjake, on one hand I think you did the right thing by telling the kids father, because he does deserve to know what his kid is doing. On the other hand, I feel like by telling the kids father, you may have subjected this kid to some level of unnecessary punishment, while knowing that what he's done is mostly harmless, save for the missing diaper, which you've admitted you don't really care about. Part of me thinks that I might have done an "I'm going to let you off with a warning this time, but if I catch you taking a diaper again, I'm going to tell your father," since you know what was likely going on here. At the same time, I feel like a better informed parent could head off potential problems that arise from kids who are closeted DLs, including the occasional "diaper kleptomaniac" that lifts diapers because as a kid, he/she can't afford them, and has no other way to get them. A parent who knows what he's dealing with can at least buy them and dole them out as a reward for good grades and prevent this kind of situation. (The parent who knows why their kid is taking diapers can prevent them from doing so, unlike the parent taking shots in the dark just regurgitating the same failed speech that didn't work the first time.) Obviously you can't deal with this situation directly, but if you can find the right Google results for your friend, that could be helpful to him in the future when this happens again.