"The God of Abraham, Isaac, and Israel never used any personal name to distinguish Him from any peers because He had no peers. Therefore, no personal name was ever needed. The only name He gave for Himself was "I am," which indicated that He is to be identified with all existence. The Greek Septuagint Old Testament of 285BC never used any sacred name for God, nor was such ever mentioned by other ancient writers such as the Israelite historians, Philo, and Josephus, or the later Eusebius, or even the Jewish Aristeas the Exegete who wrote his commentary on the Greek Septuagint. The word did not appear in any Old Testament text until the Masoretic Text of 1000AD!"
Not so. The tetragrammaton most definitely appears in Hebrew OT MSS at Qumran from the second century BC to the first century AD, as well as in MSS elsewhere. It appears frequently in Greek OT MSS from the second century BC to the first century AD. It appeared in many other religious compositions from the period. It was certainly a most ancient name used by the Israelites, appearing often in inscriptions, ostraca, papyri, and stele (such as the Mesha Stele from the ninth century BC). It appears in the seventh-century BC Ketef Hinnom text of the Priestly Benediction (from Numbers 6:24-26), the oldest copy of any OT text. The literary evidence points clearly to its later suppletion by surrogates like 'Elohim and 'Adonai, rather than a late incursion as you construe things. Although not represented as such, the tetragrammaton was referenced by Philo of Alexandria (De Vita Mosis 2.115, 132) and Josephus (Antiquitates 3.270, Bellum 5.325). It was mentioned by Clement of Alexandria, Origen, Epiphanius, and other church fathers. It was mentioned in vocalized form by Diodorus Siculus (first century BC) and other Greek writers. The MT was produced very late (c. AD 950) but that is most definitely not the first apperance of the name in the text of the OT.
Apparently, the people at my wife's hall are trying to argue that Matthew was originally written in Hebrew and the the tetragrammaton was written in it.
Nobody can be sure what language "Matthew " penned his Gospel in, I doubt it was Hebrew.
Actually there is very strong evidence that Matthew was originally written in Greek, and this is the general opinion of scholars. Matthew is really an expanded edition of the gospel of Mark, which certainly was written in Greek (among other things, formal quotations from the OT are from the LXX), embodying about 90% of the text of Mark, usually with verbatim agreement; original non-Markan material appears largely in blocks interspersed in the Markan text. The only evidence for Matthew having a Semitic original lies in late second century AD tradition; however the basis for this was the statement by Papias in the early second century AD that Matthew composed the "oracles" (ta logia) in the Hebrew language. Many have noted that this is different from the claim that the gospel itself was written in a Semitic tongue, and this accords well with the theory that the oral sayings material inserted into the Markan frame was likely first written down in Aramaic (in the NT and in common parlance, "Hebrew" was used to refer to Aramaic), in what some scholars have called "Q", which was a source utilized by the Greek author of Matthew. Even without presuming the existence of a "Q" document as a common source for Matthew and Luke (i.e. on the theory that Luke used Matthew), there would have been a source for the original sayings material incorporated into the First Gospel. To complicate things further, there were later secondary gospels translated from Greek that circulated in the second and third centuries AD in the Hebrew or Aramaic languages, which are largely redacted versions of Matthew. These Jewish-Christian gospels circulated under such names as the Gospel of the Ebionites, the Gospel of the Nazoreans, the Gospel of the Hebrews, etc., each claiming to be the "Hebrew original" of Matthew.
The people in your wife's hall are probably half-remembering Watchtower articles about the gospel of Matthew that reference George Howard's work on the medieval Hebrew version of Matthew copied by Shem-Tob ben-Isaac ben Shaprut. Shem-Tob's version is interesting for including a surrogate (the letter he with two short strokes) for the tetragrammaton within the text of Matthew (note that this is NOT the tetragrammaton per se but a symbol for it). It thus anticipates the many later Hebrew translations of the NT that (innovatively) insert the tetragrammaton or a symbol for it into the text (many of the "J" references cited in the 1984 Reference edition of the NWT). Howard however claimed that the Shem-Tob text is primitive, or at least preserves many primitive features. The Society takes this as proof, or at least strongly substantiating evidence, that Matthew was written originally in Hebrew and had the tetragrammaton in the text. Howard is more circumspect in his suggestions, finding an early date (i.e. within the first four centuries AD, possibly representing the text of the first century AD) feasible, with the gospel originating in an unidentified Jewish-Christian group. Howard's suggestions however have been met with much criticism (see Petersen, JBL 1989 and Shedinger, CBQ 1999). Others have pointed out that Shem-Tob shows dependence on gospel harmonies and is thus hardly representative of an early text of Matthew, as well as evidence that a translation from Greek underlies the text. For instance, Matthew 1:23 in Shem-Tob preserves the explanation of the meaning of the Hebrew name Immanuel (betraying a Greek origin of the text, as such an explanation is needed in the Greek but wholly unnecessary in Hebrew). Another telling example is Matthew 6:28 in Shem-Tob, which refers to how the lillies "grow, they neither spin nor weave". The Greek vorlage for "they grow" is auxanousin which occurs in the Majority Text of the verse; however this is probably a copyist error for ou xenousin "they do not card" which appears in the original text in the Codex Sinaiticus and which is probably original to the gospel since v. 26 has a similar three-part saying (neither sow, nor reap, nor gather into barns || neither card, nor spin, nor toil). The reference to weaving OTOH is found only in the Western Text of Luke 12:27 (e.g. D) and in the Old Syriac and the Old Latin; this is thus another likely secondary development. So Shem-Tob here not only embodies a harmonistic reading (which itself is probably secondary) but also probably a copyist error only possible in the Greek. It is possible that Shem-Tob is a descendent of one of the Jewish-Christian gospels translated from Greek, but Shem-Tob does not closely match the descriptions of them given in the church fathers.