Funny Joke

Do you think they called the 'Saw' films saw so that people would say:
"Did you see Saw?"
"Yeah I saw Saw."
"Did you see Saw 2?"
"I saw Saw 2 too"
"Did you see Saw 3?"
"No but I saw Saw 4"
"Why would you see Saw 4 before you saw Saw 3 for?"