Hi Geoff,
My interpretation is that the Facilitator can indeed choose to propose someone else if an objection is raised, even if not valid (we assume that the Facilitator, in this case, didn't see it). Anyone can ask to test the objection but only in the Integration Step, which means that if the Facilitator choose not the integrate the objection and to propose someone else, nobody can ask to test the objection.
If you think the person is not a good Facilitator, you may.. well.. ask for an election