not that anything associated with Rome has always been bad. The Council of Nicaea was all bishops from the Empire (who were in the 'orthodox' majority, anyway), and not controlled by the Roman Archbishop, ie Pope. I don't think Constantine had input into the choice of books, either - he himself wanted a suitable official religion, and told the bishops to come up with an agreed answer, but was no scholar himself (I'm not even sure if he was baptised).
Fundamentalists' objections to the RC church stem from those made by Luther, Calvin etc. in the Protestant Reformation, which were that the Catholic church had become a power structure that claimed special insight into the 'truth' about God, and had become in many cases corrupt. They would presumably say God guided the choice of books. Plus there is a slight difference in the books of the Old Testament between Protestant and Catholic churches anyway, so they can point at a later decision by Protestants to not accept the Nicaean decision as 'infallible'.