Although the Second Nun primarily narrates her tale of Cecilia in a very objective-seeming third person voice, she does insert the occasional "as I writen fynde." What's up with that? Well, remember that the Second Nun announced in her Prologue that she was basically just parroting "the wordes and sentence / Of hym that at the seintes reverence / The storie wrote" (81-83). Unlike some of the other characters who make this claim (ahem, Chaucer!), this narrator actually seems very concerned with keeping up the appearance that she's narrating from a legend she's read somewhere.
A written source for her tale adds more authority to the narrator's voice. Since she's a woman, gender politics may be at work here: perhaps the narrator feels uncomfortable narrating a lengthy tale on her own, and wants the support of male "auctoritas," or authoritative texts, to support her. This explanation might also account for why she inserts a citation from Saint Ambrose in praise of Cecilia's crown, instead of just praising it herself. She uses the male authority to strengthen her own, and to authorize a potentially subversive female figure.