The U.S. federal Megan's Law came in ten years ago, not seven. And over that period all the crime figures have dropped -- for example, in 1996 the property crime rate was 4,451 per 100000 inhabitants and in 2004 it was 3,517.1 per 100000 inhabitants. That's a drop of nearly 21%. So if your 16% figure is accurate then offences on children didn't drop by nearly as much as other categories of offences.
Meanwhile, in the U.S. the number of convicted sex offenders who are registered with the authorities (so that someone knows who they are, police can keep an eye on them, etc.) is 80% (in the UK it's 97%). That means that one in five sex offenders in the US no one has the faintest idea where they are or is monitoring them in any way.
I don't know where your documentary got its figures from. Research suggests that about one-third to one-half of sex offenders subjected to community notification experience events such as the loss of a job or home, threats or harassment, or property damage (Levenson, J. S., & Cotter, L. (2005b). The impact of Megan's Law on sex offender reintegration. Journal of Contemporary Criminal Justice, 21(1), 49-66.; Tewksbury, R. (2005). Collateral consequences of sex offender registration. Journal of Contemporary Criminal Justice, 21(1), 67-82.). Physical assault seems to occur in 5-16% of cases and about 19% of sex offenders report that these negative consequences have affected other members of their households.