1. IEEE Std 802.1D-2004, "IEEE Standard for Local and metropolitan area networks—Media Access Control (MAC) Bridges":
Section 17.4, Port Roles: This section formally defines the RSTP port roles. It specifies: "An Alternate Port...receives more useful Designated Bridge information from another Bridge than the Root Port...". It also defines a Backup Port: "A Backup Port...receives more useful Designated Bridge information from the same Bridge it is on...". This directly contradicts the question's statement for an Alternate Port.
2. Nokia 7750 SR OS Services Architecture Guide, Release 21.10.R1:
Chapter: Spanning Tree Protocol (STP), Section: RSTP: The documentation defines the port roles consistent with the IEEE standard. It describes an Alternate port as providing "an alternate path to the root bridge from the root port." It defines a Backup port as providing "a redundant path to a segment where another bridge port already connects... A backup port exists when a bridge has two or more connections to the same segment... The backup port is the port that is not the designated port." This confirms the question is describing a Backup Port's relationship, not an Alternate Port's.