As those who recorded Mohammads life were Muslims, is there any historical evidence to suggest that their reports are accurate or could they have been exaggerated? For example this copypaste from Wikipedia:
Attempts to distinguish between the historical elements and the unhistorical elements of many of the reports of Muhammad have not been very successful.[39] A major source of difficulty in the quest for the historical Muhammad is the modern lack of knowledge about pre-Islamic Arabia.[10] According to Harald Motzki, "On the one hand, it is not possible to write a historical biography of the Prophet without being accused of using the sources uncritically, while on the other hand, when using the sources critically, it is simply not possible to write such a biography."[2]
Historian Michael Cook takes the view that evidence independent of Islamic tradition "precludes any doubts as to whether Muhammad was a real person" and clearly shows that he became the central figure of a new religion in the decades following his death. He reports, though, that this evidence conflicts with the Islamic view in some aspects, associating Muhammad with Israel rather than Inner Arabia, complicating the question of his sole authorship or transmission of the Qur'an, and suggesting that there were Jews as well as Arabs among his followers.[40] For Patricia Crone, a single Greek text written at around the time of Muhammad's death provides "irrefutable proof" that he was a historical figure. There is also, she says, "exceptionally good" evidence that Muhammad was an Arab political leader and prophet. She says we can be "reasonably sure" in attributing all or most of the Qur'an to him. She takes a view that Muhammad's traditional association with the Arabian Peninsula may be "doctrinally inspired", and is put in doubt by the Qur'an itself, which describes agricultural activity that could not have taken place there, as well as making a reference to the site of Sodom which appears to place Muhammad's community close to the Dead Sea.[41]
In their 2003 book Crossroads to Islam, Yehuda D. Nevo and Judith Koren advanced a thesis, based on an extensive examination of archaeological evidence from the early Islamic period, that Muhammad may never have existed, with monotheistic Islam only coming into existence some time after he is supposed to have lived. This has been described as "plausible or at least arguable" and employing a "very rigorous historical methodology" by David Cook of Rice University, but has also been compared to Holocaust denial by historian Colin Wells, who suggests that the authors deal with some of the evidence illogically.[42][43]
Muhammad Sven Kalisch, a Muslim convert and Germany's first professor of Islamic theology, has expressed the view that the Prophet Muhammad probably never existed.[44] Similar views were also held by other scholars too as Professor Muhammad Sven Kalisch quotes in his conclusions. There are many such views doubting the historicity of Muhammed. Another example is the case of Hans Jansen, a Dutch scholar, who too has the opinion that the evidences supporting the historicity of Muhammad are lacking.[45]
Popp (2004/5) proposed that both Muḥammad and ‘Alī originated as titles given to Jesus Christ by Syriac Christians in the Sassanid Empire (i.e. muḥammad "blessed" being the equivalent of the benedictus (ευλογηµένος) of the New Testament). In a numismatic study, Popp identified coins dated to AH 16 inscribed with mḥmd but lacking the rasūl allāh that later became common. Popp adduced Arabo-Sassanid and Syrian coins inscribed with MHMT in Pahlavi script, and also partly with mḥmd in Arabic script, in some cases combined with Christian symbolism.[46] Heger (2008) argues that Muḥammad "the blessed one" being a title of Christ does not necessarily preclude the historicity of the prophet of Islam. It rather opens up a scale of possibilities summarised in three alternatives to the default assumption of the historicity of a Muhammad recognizably similar to the hadith accounts, the Islamic tradition on the life of Muhammad is entirely legendary, Muhammad is historical, but was active roughly a century later than suggested by Islamic tradition, there were two distinct people, both given the epithet Muhammad or "blessed", one active in the early 7th century, and author of the Meccan suras, and the other the Mamed of Johannes Damascenus, author of the Medinian suras
Do these theories which go against the traditional Muslim narrative of Mohamamd hold any water?
So unfortunately this wiki article is a whole hodgepodge of good, bad and ugly in the historiography of Muhammad and early Islam.
The first paragraph is fine. It is universally recognized in academic scholarship that the Islamic sources for the biography of Muhammad are of dubious provenance. These accounts (e.g. the hadith (collected sayings and descriptions of the prophet), the sira (prophetic biography), and the exegesis of the Quran) weren't collected and written down until hundreds of years after Muhammad's death. Though they have their defenders, these sources are very much of suspect reliability and everyone in the field has to account for that, one way or the other.
Everything beyond the first paragraph, however, is at the far fringe of revisionist historiography. Much of it is actually presented in a misleading way as well.
So when the article writes:
For Patricia Crone, a single Greek text written at around the time of Muhammad's death provides "irrefutable proof" that he was a historical figure.
Actually she cites many documents that provide such evidence. Nor is there much doubt about the provenance of the Quran or the "Constitution of Medina" which she also cites as being genuine products of Muhammad. Rather she cites a lone Greek document that may have been written during Muhammad's lifetime as being, by itself, such a confirmation. In any event, it's far easier to read Crone's views in her own words here.
Still dealing with that second paragraph, Michael Cook and Crone have long been proponents of a North Arabian or Palestinian origin for Muhammad and Islam. They cowrote Hagarism which was the origin of much of the revisionist thinking on this (though they later repudiated Hagarism, as I understand it). While their criticism of the sources has been widely acknowledged their proposals for alternatives to the traditional account (e.g. Quraysh being based around the Dead Sea) are not well accepted.
Everything after the second paragraph is basically non-sense.
based on an extensive examination of archaeological evidence from the early Islamic period
That would be impossible because there has never been an "extensive" archaeological examination of the relevant sites in the Hejaz.
the Prophet Muhammad probably never existed.[44] Similar views were also held by other scholars too
Sure, there are some other scholars that hold that view. But the overwhelming majority of them, including several of the scholars cited earlier in the article, do not. Again, it flies in the face of the documentary evidence that we do have, and the cited article from the Wall Street Journal, to my reading, merely asserts Kalisch's view that Muhammad didn't exist without supporting it. It specifically mentions that many of his colleagues, who are predominantly non-Muslim, do not agree with him.
I don't even know where to start with that last paragraph as it flies in the face of every other analysis of the numismatic and other evidence that I've ever come across. It strains credulity to think that coins being struck by Arab Muslim rulers, who had Christian subjects (and indeed, those Christians were likely striking the coins themselves given the continuity in administration after the conquests) were somehow just confused about the name of Jesus.
The "two Muhammads" idea is a new one to me and also strikes me as being blathering nonsense. Unfortunately the author who proposes it seems to only write in German so I can't say much more about his ideas except to say that as far as I'm aware they are his and his alone.
For a much more even-handed account of the problems with using traditional Islamic sources and the current state of the historiography of these questions, see Robert Hoyland's article Writing the Biography of the Prophet Muhammad: Problems and Solutions which you can read as a PDF here.