Protecting the Rights of Musicians Act - Amends the Communications Act of 1934 to exempt from retransmission consent requirements under which cable systems or other multichannel video programming distributors (MVPDs) are prohibited from retransmitting the signal of a television broadcasting station without the originating station's consent (which is generally obtained through a retransmission consent agreement under which the cable system or other MVPD provides a negotiated payment or other consideration to the station in exchange for retransmission authority) the retransmission of the signal of a television broadcast station if the licensee of such station is also the licensee of an AM or FM radio broadcast station that has transmitted a sound recording over such radio station without providing compensation for all programming carried over the signal.