Estrada & Owen filibuster update

The American Center for Law and Justice says: “Change the rules and vote!” Sounds too good to be true:

The ACLJ determined that there is existing legal and Senate precedence that would permit the majority to act - relying on a simple majority - 51 Senators - to change Rule XXII, bring an end to the filibusters, and call for a vote by the full Senate on Miguel Estrada and Priscilla Owen - two nominees who are being blocked.

But…and correct me if I’m wrong…under current rules, couldn’t the Democrats filibuster the rule change also?