
Its good to know that finally they know you are a good guy

But it might have been worthwhile to have asked them what was taking all this time, since there may be something behind all this (the HO guys are professionals and they do things for a reason!), maybe a mistaken identity or something, which can come and bite you over and over again (I sincerely hope not!) in future too.
So given he/she was interviewing you, with the benefit of having them before you, you could have asked them for any info on this unusual delay and checks, so that at least you can get it cleared formally for good for the future at least now?
Just a thought.