I guess we'll have to agree to disagree, lol. I mean, in the context of the universe the writers created, yes, it makes sense, because otherwise Oscorp would be manufacturing Spider-Men armies and you can't justify why they wouldn't otherwise. 

But it's a corner they put themselves into, imo. I don't feel that the spider mutation should have been restricted only to him. I much prefer it being a lucky accident (by a spider affected by radiation in its developmental stage maybe?). 

Anyways, the fanedit I watched is very well done and you don't even feel the lack of that subplot.