A new post on the TSA blog gets the logic behind the strip/grope combination correct.
[I]f you’re selected for AIT and choose to opt‐out, we still need to check you for non‐metallic threats. That’s why a pat‐down is required. If you refuse both, you can’t fly.
Any alternative allows someone concealing something to decline the strip‐search machine, decline the intimate pat‐down, and leave the airport, returning another day in hopes of not being selected for the strip‐search machine. The TSA reserves the right to fine you $11,000 for declining these searches.
So the question is joined: Should the TSA be able to condition air travel on you permitting someone to look at or touch your genitals?
I’ve argued that the strip/grope is security excess not validated by risk management. It’s akin to a regulation that fails the “arbitrary and capricious” standard in adminstrative law. But the TSA is not so constrained.