It's quite unclear to me what point David is trying to make about this genitive participial construction with verbs of perception.
For what it's worth, I would like to note a couple things: (1) It seems to me that the relationship between the MT and the LXX of this verse is less than obvious: certainly the LXX text is much older than the MT; even if the LXX does represent the same sense as the MT, the construction of the Greek can convey the same sense without emulating the kind of construction (e.g. "they heard when he said this" is not essentially different in meaning from "they heard him say this").
It may also be useful to some to have grammatical references for the usage of genitive + participial genitive with a verb of perception:
416. The supplementary participle with verbs of perception and cognition is better preserved in the NT. In classical Greek the participle takes the nominative case if it refers to the subject of the verb (ὁρῶ ἡμαρτηκώς); the accusative (or genitive) if it refers to the object. Except with passive verbs the nominative does not appear in the NT referring to the subject (ὅτι is substituted Mk 5:29, 1 Jn 3:14).
(1) Verbs of perception: to see (βλέπειν, θεωρεῖν, [ὁρᾶν,] ἰδεῖν, θεάσασθαι, ἑωρακέναι, τεθεᾶσθαι, ὄψεσθαι, κατανοεῖν): Mt 24:30 ὄψονται τὸν υἱὸν τοῦ ἀνθρώπου ἐρχόμενον, cf. 15:31, Mk 5:31, Jn 1:32, 38, H 3:1f., etc.; with ὄντα A 8:23, 17:16, with ellipsis of this ptcp. (cf. §414; also class., Krüger §56, 7.4): Jn 1:50 εἶδόν σε ὑποκάτω τῆς συκῆς, Mt 25:38f. σε εἴδομεν ξένον, ἀσθενῆ (ἀσθενοῦντα is preferable, BD), ἐν φυλακῇ etc., cf. 44; A 17:22 ὡς δεισιδαιμονεστέρους ὑμᾶς θεωρῶ (no further examples of this ὡς are found with verbs of seeing; but cf. infra (3) ὡς ἐχθρὸν ἡγεῖσθε 2 Th 3:15 ‘as if he were an enemy’ [s. also §157(3)]; the meaning of A 17:22 must therefore be: ‘as far as I see, it appears as if’ [softening of the reproach]). Occasionally with the verb ‘to see’ and other verbs of this type the ptcp. is more independent of the object and constitutes an additional clause, while the obj. and verb are fairly complete in themselves: Mt 22:11 εἶδεν ἄνθρωπον οὐκ ἐνδεδυμένον etc. = ὃς οὐκ ἐνεδέδυτο, Mk 11:13 ἰδὼν συκῆν ἀπὸ μακρόθεν ἔχουσαν φύλλα (‘which had …’). For ὅτι after ‘to see’ s. §397(1).—Ἀκούειν is no longer frequent with ptcp.; when the content of what is heard is stated, its rivals are the acc. with inf. and especially ὅτι (§397(1)). Examples of the acc. with ptcp.: Lk 4:23 ὅσα ἠκούσαμεν γενόμενα, A 7:12, 3 Jn 4, 2 Th 3:11 (Mk 5:36? however B τὸν λόγον τὸν λαλούμενον, D has yet another reading); a distinction between the inf. and ptcp. as in class. (the ptcp. denoting more the actual fact, the inf. hearsay, K.–G. ii 68) probably cannot be claimed for the NT. The acc. construction appears also (A 9:4, 26:14) for the class. gen. construction which is not frequent outside of Acts: Mk 12:28 ἀκούσας αὐτῶν συνζητούντων, 14:58; Lk 18:36 ὄχλου διαπορευομένου, Jn 1:37, A 2:6, 6:11, etc.; 11:7 and 22:7 ἤκουσα φωνῆς λεγούσης μοι, for which 9:4 and 26:14 (E has gen.) have φωνὴν λέγουσαν, although φωνή refers to the speaker and not to what was said; cf. §173(2).