When you consider the original Greek, it's not an especially contentious proposition. There are many omissions in the gospels where the word considered to be 'omitted' (e.g. an adjective) would radically alter not only the meaning of the sentence, but also necessitate a different form of the noun than appears in the manuscript. (The inverse is also a helpful way of detecting omitted words: when a declension is used which is only required if a specific form of a word was also supposed to be present.)

Matthew:

> ῥαπίζει εἰς τὴν δεξιὰν σιαγόνα σου

> rhapizei eis tēn dexian siagona sou

> shall strike on the right cheek of you

Luke:

> τύπτοντί σε ἐπὶ τὴν σιαγόνα

> typtonti se epi tēn siagona

> striking you on the cheek

If you change Luke to:

> τύπτοντί σε ἐπὶ τὴν δεξιὰν σιαγόνα

We're simply changing "tēn siagona" ("the cheek") to "tēn dexian siagona" ("the right cheek"), which is how it appears in Matthew. The entire way which Luke rewrites SP is in general interesting. Here's Matthew:

> ἐγὼ δὲ λέγω ὑμῖν μὴ ἀντιστῆναι τῷ πονηρῷ· ἀλλ’ ὅστις σε ῥαπίζει εἰς τὴν δεξιὰν σιαγόνα σου, στρέψον αὐτῷ καὶ τὴν ἄλλην·

> I however say to you, not to resist the evil person. Instead, whoever you shall strike on the right cheek of you, turn to him also the other;

and

> καὶ τῷ θέλοντί σοι κριθῆναι καὶ τὸν χιτῶνά σου λαβεῖν, ἄφες αὐτῷ καὶ τὸ ἱμάτιον·

> and to the one willing you to sue and the tunic of you to take, yield to him also the cloak.

Luke combines these into one more elegant verse:

> τῷ τύπτοντί σε ἐπὶ τὴν σιαγόνα πάρεχε καὶ τὴν ἄλλην, καὶ ἀπὸ τοῦ αἴροντός σου τὸ ἱμάτιον καὶ τὸν χιτῶνα μὴ κωλύσῃς.

> To the one striking you on the cheek, offer also the other; and from the one taking away your cloak, also the tunic do not withhold.

But, as Winks and others point out, we start to see him corrupting native praxis and idioms in the manner of a foreigner ill acquainted with the region. "Living on a wing and a prayer" would become "existing on a prayer and a wing" to Luke.

It's certainly plausible that Luke did not understand the cultural significance of the word. He was, after all, a man from a different part of the world, writing a generation after the fact, having by his own admission not witnessed any of the events. The bet you're making is analogous to betting that a Frenchman transcribing and interpreting a speech made by a German politician from 100 years previously is going to be a nuanced understanding of the cultural mores.

Finally, you've tried to dodge the issue of Luke's authorial intent, but it's important. Luke wrote for a Gentile audience. Matthew for Jews. Mark for Romans.

It seems like you might be aware that Luke deliberately smoothed some of the sharp edges of the earlier gospels (to the point of being totally brazen in places. As Guignebert wrote, "A hagiographer of [Luke's] type never bothers much about common sense in inventing the circumstance he requires."), but Luke frequently displays a lack of understanding of the society about which he writes. He frequently summarises a lot of Jewish tradition when Matthew goes deep on detail, or omits important context altogether.

A good example is his treatment of the Pharisees. Whilst Mark and Matthew share meaningful discussion between Jesus and the Pharisees over the traditions of oral law, Luke skips it altogether, either because he doesn't understand or doesn't see the relevance. But to scholars reading Mark and understanding the various early creeds of Christianity, it's plain that Luke and John are the final couple of kids in a big game of telephone. Luke is not fearful of Judaism as Matthew and Mark were, so his gospel contains some of the stern criticisms and pointed remarks of Mark and Matthew, whilst also praising them or ignoring them at points which are divergent with the other accounts. To Jesus, and anyone writing about the life of Jesus in the region, the Pharisees were an authoritative shadow hanging over everything. Not understanding that, or ignoring that in order to reframe Jesus's teachings, certainly makes Luke an easier and more universally applicable read. But it makes it further from Christ's message, not closer to it. It's never more apparent than in the beatitudes. Matthew says "Blessed are the poor in spirit," but Luke redacts and rephrases to "Blessed are you who are poor."

The writers of the gospels had to overcome the significant incongruity of Jesus the human apocalyptic preacher, making no claims of divinity, believing that the end times were just around the corner (Mark), and the fact that the world did not end, and Jesus was executed. This is why we have the prophecy-fulfilling claptrap of Matthew and Luke: it's all apologetics written years later, and largely at odds with the explicit mission of the earliest and most historically accurate gospel: to ensure adherence to the old law.

It's almost unequivocal that Luke's gospel is a better reflection of the message of Jesus as we know it today. That's because Luke to some extent invented that message. But for anyone thinking about the gospels, it's very tough to ignore the author's serious lack of understanding of the context and times about which he writes, and it makes claims that we can ignore the meaning contained within the expansive and detailed passages Luke rewrites fanciful in the extreme.