There is no requirement for the Governor to call a special session. Legislatures can do it on their own. The Governors have no role regarding federal elections. The Legislatures have sole and final authority.
Agreed, in terms of Federal law.
However, state legislatures may incorrectly feel bound to respect state laws, even if they were erroneous or unconstitutional.
It is my personal opinion that since this is a Federal and constitutional matter, and since innate authority rests with the state legislature, they are in fact authorized to act - by the constitution itself.