He did have his gadget available to him, and he was there for the assembly. He probably had an idea of where it was, but didn't know exactly since he didn't do the sewing. *shrug*
But you're right - I don't think they thought the relationship of those two actions through. At the least he should have been like "Only I can do that b/c of my analysis skills!" or "Whatever, that's not impressive"
Yeah later on Iori specifically says that he's surprised that someone can do it without the use of gadgets. But Inu definitely acts like he's never seen that before, which doesn't make any sense at all...
I guess that's the first legitimate plot hole discovered then?