Objections to electoral votes are the basis of the counting of votes, not constitutional eligibility. Two pages prior to what you quoted is the section that says no federal agency or office vets candidates as to qualifications. The next paragraph says that states and state laws administer the elections of federal official within those states. Congress does NOT have a constitutionally designated function of vetting eligibility ... and especially not the sole eligibility to do so. Such powers not designated to the Federal government fall to the states or people according to the 10th amendment. This explains why states have ballot laws and affadavit requirements for presidential ballots. It also means Lakin has a constitutional right to challenge the constitutional authority of the resident of the White House.
“Objections to electoral votes are the basis of the counting of votes, not constitutional eligibility.”
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I understand that’s your position, but the report says something quite different. I quoted it above, and I will quote part of it again. It makes it perfectly clear that, in 2008, the power to object on the grounds of eligibility was not exercised:
“It appears from the record that no Member of the House or Senate of the 111th Congress, in joint session for the purpose of counting and certifying the electoral vote, raised or forwarded any objection to the electoral votes of (then) President-elect Obama on the grounds of qualifications, or otherwise.”