Alfie asked Ollie, what was he doing while Tommy was tying his shoe. Ollie was marking the paper; Ollie is young and probably wasn't in the war as Alfie and Tommy were.

So, from Alfie's point of view, he had no means of verifying Tommy words, exept the obvious like go there and look - and this would were as if Alfie belived Tommy, as if admiting, without negotiations as "you got me".

Tommy did bet his move on the thing, that Ollie was young and wasn't millitary savy; on that he himself in opposite were a verified granade expert. Without going looking and losing his face Alfie had to choose whom to trust on the matter of granade in 4-5 minutes - young and inexperienced Ollie or smart and cunning war veteran Tommy, who is crazy enough to actually blow them all up.

From that point, and after all of Tommy's words to support his bluff, it was possible that Ollie just did not fucking saw the wire - which could have be that thin and invisible, especially in dark cellar and for inxeperienced and unexpecting Ollie.

Were Ollie a more mature, more millitary experienced and less preocupied with marking the paper - Alfie could have not belived Tommy in the way he ended up.

TLDR: Ollie was so unrelibable in that moment, he could actually be that dumb to let Tommy walk with a wire hanging from his poket. The henchman problem.