That argument is one theory, highly controversial. I'm certainly not saying it doesn't play a part, but it's still a hotly debated question among experts as to what is ultimately responsible for the crime drop. Most likely, it's due to a combination of factors, for the basic reason that social phenomena like crime tend to be very complicated. We would be extraordinarily lucky if it could be pinned down a single, simple explanation.
And while the socioeconomic distribution of the population would be expected to play a part (which is certainly affected by family planning), it would be highly unlikely for progress in policing techniques not to play a part at all.
[edit: birth control and the Rowe vs. Wade abortion ruling]