So how do team leads get away with saying "Hol' up, I ain't technical" when you try to explain something?

They should not!

If they are leading a tech team, then they had want to be technical.

If they aren't technical, they shouldn't be leading a team related to technical stuff.

Depends on what you mean with "get away with". If you're asking "why is this guy not getting fired for impeding the team?", I can speak from experience. They get away with it because the managers above them either don't know what's going on, or they do but don't understand why it's a problem.

That said, in my opinion "team leads" shouldn't exist. Ideally, a team of devs would consist of grown-ups, be viewed by management as grown-ups, and the most competent devs wouldn't lead using a role but just by example. Such teams exist, but unfortunately are unstable by nature.