It never seems to be open when I walk past it in the morning, which seems a bit odd for a bakery.
I think that the trick to the 24 hour thing is that the person in charge lives above, so you can knock/ring/enter and she can be there 24 hours. It may look closed, but I think that this might be the reason ... not that I have been in there I must admit
I don't believe that this is a bagel bakery as much as a sandwich shop with a fancy name, so not that odd that custom is limited in the morning