>Their product giving false positives (unnecessary challenges for a normal browser humans commonly use) to real people is definitely their fault.

Is it TSA's "fault" that non-terrorists are subject to screening?

No, but it's entirely within TSA's hands to make that process as frictionless as possible.

(It's a different question whether zero friction is actually desired, or whether some security theater is actually part of the service being provided, but that's a different question.)

We're discussing the quality of screening here, not the act/necessity of screening itself.