I have seen DPEs make the checkride harder with a fed watching. Likely because their standard checkride is probably too easy and it wouldn't pass with a fed.
I've seen that happen twice, but those were due to office politics within the FSDO.
I had a student scheduled for a PPL checkride, and when the DPE showed up, he decided that would be a good time to inform the applicant and myself that someone from the FSDO was going to be present to for his annual renewal.
Once the oral got started, the FSDO inspector basically hijacked the checkride (the student told me that the DPE asked maybe three or four questions before the FSDO took over), and the inspector proceeded to fail the student on the oral for reasons that both the student, myself, and the owner of the flight school thought were complete BS.
A couple of weeks later, a different student was doing an instrument checkride with the same DPE, and the same FSDO inspector showed up again, and did the exact same "hijack oral after a couple questions, find BS reasons to fail applicant" routine he'd pulled with my student.
Both of those students had no trouble passing the checkride on the retake (without the FSDO inspector present), and from what we were told later, both incidents were due to the DPE and FSDO not getting along (for reasons that weren't explained), which eventually lead to the FSDO going out of their way to make sure the DPE wasn't reinstated as an examiner.