Wettstein (1:346) thinks the change to the genitive occurred "so that αὐτῷ might not appear twice in the same phrase," a sentiment Griesbach (1:83–4) affirms, adding that V/031 omitted the first αὐτῷ for the same reason, and concludes, "That the text was intentionally altered is clear from this, that in verse 5, for the same recurring reason, the same variety of reading is also discovered in nearly the same manuscripts." Kühnöl (226) calls the pronoun αὐτῷ after the verb ἠκολούθησαν redundant but in accordance with the style of the Hebrews and not unknown to pure Greek writers, and agrees that the genitive alteration arose "in order to avoid repetition of the pronoun αὐτῷ."
Fritzsche (304–5) calls the genitive "a wrong correction by one who faltered at the double occurrence of the dative, and about this there can be very little doubt for this very reason, that also elsewhere (see comments below on Matt 8:5, 28, Mark 5:2, and above on Matt 4:16) such places were wrongly handled in order to remove this stumbling block." For evidence of the same corrective phenomenon, Bloomfield (Annotations, 7) adds Matt 9:27, "where some copies substitute the genitive; others, as B D, remove the second αὐτῷ." Meyer (174) rejects καταβάντος δὲ αὐτοῦ as "a mere correction, like the similarly attested εἰσελθόντος δὲ αὐτοῦ" in 8:5.
The scribal agitation at the grammatical construction generally seems to have been remedied by (1) altering the dative construction to a genitive absolute, (2) omitting the following "superfluous" dative pronoun, or (3) altering the dative construction to a finite verbal form.
(1) Altering the dative construction to a genitive absolute:
Matt 8:5 εἰσελθόντι δὲ αὐτῷ ... προσῆλθεν αὐτῷ(2) Omitting or altering the following "superfluous" dative pronoun
VS. εἰσελθόντος δὲ αὐτοῦ ... προσηλθεν αὐτῷ (ℵ B C* Z f1.13 33)
Matt 8:28 ἐλθόντι αὐτῷ ... ὑπήντησαν αὐτῷ
VS. ἐλθόντος αὐτοῦ ... ὑπήντησαν αὐτῷ ([ℵ] B C Θ f1.13 33vid)
Matt 9:28 ἐλθόντι δὲ ... προσῆλθον αὐτῷ
VS. ἐλθόντος δὲ αὐτοῦ ... προσῆλθον αὐτῷ (700)
Matt 21:23 ἐλθόντι αὐτῷ ... προσῆλθον αὐτῷ
VS. ἐλθόντος αὐτοῦ ... προσῆλθον αὐτῷ (ℵ B C D L Θ f1.13 33)
Mark 5:2 ἐξελθόντι αὐτῷ ... ἀπήντησεν αὐτῷ
VS. ἐξελθόντος αὐτοῦ ... ὑπήντησεν αὐτῷ (ℵ B C L Δ Θ f1.13 565)
Matt 8:23 ἐμβάντι αὐτῷ ... ἠκολούθησαν αὐτῷ(3) Altering the dative construction to a finite verbal form
VS. ἐμβάντι αὐτῷ ... ἠκολούθησαν (ΟΜ. αὐτῷ) (565)
Matt 9:27 παράγοντι ... τῷ Ἰησοῦ ... ἠκολούθησαν αὐτῷ
VS. παράγοντι ... τῷ Ἰησοῦ ... ἠκολούθησαν (ΟΜ. αὐτῷ) (B D 892)
Luke 8:27 ἐξελθόντι δὲ αὐτῷ ... ὑπήντησεν αὐτῷ
VS. ἐξελθόντι δὲ αὐτῷ ... ὑπήντησεν (ΟΜ. αὐτῷ) (p75 ℵ B E W Ψ Ξ f1 33)
Matt 9:28 ἐλθόντι δὲ ... προσῆλθον αὐτῷThat all of the questionable cases either occur in Matthew or conceivably derive from Matthean material (Mark 5:2 and Luke 8:27 parallel Matt 8:28) suggests a Matthean stylistic option that scribes frowned upon and variously sought to change to a more standard construction. Otherwise, a great number of scribes not only altered the more common form to a less common one, but also were remarkably selective in doing so. Hence no internal rule of textual criticism can admit the priority of the genitive construction to the dative one, and furthermore the internal rule only suggests the external excellence of those manuscripts that retain the less common (i.e. harder) readings both in Matt 8:1 and in the other examples cited above.
VS. καὶ ἔρχεται ... καὶ προσῆλθον αὐτῷ (D)
Luke 8:27 ἐξελθόντι δὲ αὐτῷ ... ὑπήντησεν αὐτῷ
VS. καὶ ἐξῆλθον ... καὶ ὑπήντησεν αὐτῷ (D)