In my opinion TimDrakeRobin got it completly correct. The Venom costume is an alien that mimmiced Spidey's costume through the best of its understanding of Peter's thoughts. For a while, it even mimmiced street clothes as it still does with Eddie Brock. After Spidey got rid of the alien for the second time using a church's bell tower it left Peter. Hence it's hatered toward Peter Parker and everyone he knows since it did share his thoughts for a while. Reed Richards ( Mr Fantastic) helped him get rid of it the 1st time. After getting rid of the alien costume Peter did wear an identical costume that I believe Reed Richards made for him for a very short time. So, technically, they can make it look like the red and blue costume though in my opinion it "SHOULD" be the black and white one since thats what it interpreted as Spidey's costume when his red and blue one was hanging on by threads. ( Sorry, I've an extensive comic collection too, lol.)
Dave
Dave