The most interesting thing about this (to me , anyways) is the WT's not giving any sources for the idea of a guardian angel. They don't want anyone doing any further research.
From the BECNT-Acts commentary (Darrell L. Bock, pp. 428-9):
Some [in the Acts account] take Rhoda's announcement more seriously and suggest another alternative: that "his angel" is present. Tobit 5:4-16 records an angelic visit by Raphael to heal a blind man but lacks the idea of his being a particular person's angel. Tobit 5:22 has a specific angel accompany a person (on angels, Gen 48:16; Ps 91:11; Dan 3:28; 6:22; Matt 18:10; Heb 1:14; Rev 2-3 has an angel associated with a church). The later rabbinic text Gen. Rabbah 78 [50a] on Gen[esis] 33:10 has a specific personal angel whose look matches that of the person he protects (Str-B 2:707-8; L.A.B. 59.4; T. Jac. 1.10; in early Christian literature, Herm. Mand. 6.2.2; Johnson 1992: 213). It may be that this alternative is seen as indicating that, in the view of some, Peter is already dead and his angel is now present, having appeared after his death. . . The suggestion seems to assume that they simply refuse to accept the possibility that Peter has escaped. Those inside the room do seem to have rejected the idea that God would spare Peter with a miraculous escape. They have been praying for some other outcome (see v. 5). Thus, the idea of a communication from beyond becomes an option, although it is not clear that they think Peter is already dead.
I notice that whenever a non-WT commentary gives a source from the apocrypha (in this case Tobit), the Society's commentary will usually not cite it. I think they are afraid someone might actually look it up and then get interested in reading the apocryphal books.
Edited to add:
The NAC-Acts commentary (John B. Polholl, p. 282) has this:
This response [that it is "his angel"] reflects the Jewish belief that each person has a guardian angel as his or her spiritual counterpart. It was believed that one's angel often appeared immediately after the person's death, and that idea may lurk behind the response to Rhoda.