BB, What I'm saying is this guy wants to use a 1 1/2" Vent for a WC. The WC is 3", you need to replace a 3" water slug with a equal amount of Air or you create lower pressure or what many call a vacuum. This makes no sense unless there is some proof this works. This water first enters the 3" line pushing air ahead of it then an equal amount of air must replace the water. Not doing this will upset the +/ - 1" of atmospheric pressure needed to balance the P traps in the Lav.
Hell, why not use a 1/4" vent line ? All you need is an air compressor.
The Code is Law when the word ' Shall ' is in that part. The Code has allot of ' Mays ' and ' Shoulds ' in it. May, is to ask permission and Should, means its up to you.