Bad human resume text and overuse of unmodified LLM output are both detectable, but they are detectable because they are bad in quite different ways.
Regarding the original resume reader's notion that they can detect LLM text with a high degree of accuracy, it is not their LLM output detection specificity I would take issue with (similarly, despite stating validation is critical, I would bet you, too, are pretty confident when you see an entire page of blogspam or marketih copy that you regard as LLM generated despite it rarely being marked as such). Rather, it is their sensitivity, as I am sure occasional use and especially slightly modified output from LLMs gets by them now and again without them knowing.