No, he is not wrong. There is no constitutional requirement that the President pro tem of the Senate belongs to the majority party, or that he is the longest serving member. Majority Leader of the house and Senate are not Constitutional offices, and are only voted upon by the members of the majority party, i.e, Republicans. Speaker of the House and President Pro Tem are Constitutional offices, and are elected by the committee of the whole ( in other words, all members of the House or Senate).
As a practical matter, these positions are always held by a member of the majority party because no Republican would vote for a Dem majority leader, and vice versa.
The truth is, there is no Constitutional requirement that either the Speaker of the House or the President Pro Tem of the Senate be a Senator or Representative. There was some concern at one point that if the Dems won back control of the House, they might elect Beelzebubba as Speaker...