The history of the elites in this period is quite well documented from multiple sources. There are some minor royals - third and fourth sons - where little is known other than some titles and lands granted, but the historical record is both comprehensive and considered accurate, particularly for those whose stories were quite shocking like the 7th wife of Philip II (Cleopatra Eurydice, the young woman whose remains are being discussed), whose death may have been suicide, or a murder made to look like suicide...
The thread they're pulling on seems to start here, from the paper:
> There is a unanimous agreement that Tomb III belongs to King Alexander IV, the son of the Great Alexander. This is important because it shows that the Great Tumulus belongs mainly to the Kings of the Argead dynasty, and this contributes significantly to the identification of Tombs I and II as belonging to either Philip II or Arrhidaeus
If accept that unanimous agreement is well-founded, and it is beyond any reasonable doubt that Tomb III belongs to the son of the Great Alexander, then it seems very likely that Tombs I and II must belong to Philip II or Arrhidaeus. The paper seems to then try and work out which one belongs to who.
Now you look through the historical record of each, and you identify that there are multiple sources indicating that Philip had a young wife (Cleopatra Eurydice), who had a young son who was murdered [1]. Then you find a tomb that along with a male, has a younger female with an infant son interred. There is no other known tomb that contains similar remains. That matches Philip II, but does not match Arrhidaeus.
You then look at the other tomb, and realise those remains better matches Arrhidaeus.
This is not proof in a scientific sense, it's not irrefutable, but you have to ask if the young woman and infant are not Cleopatra Eurydice and her son Caranus, who exactly are they? Which other persons match the known historical records? If they're people from outside of the known record, just how likely is it that they would be buried in this specific context of a tomb neighboring Alexander IV? Unless you then want to unpick that assumption of Alexander IV of course, which you're entitled to do, but you're now pushing back against a collective assumption with some significant weight (and I presume, evidence), behind it.
The rest of the paper starts to pull at the logic of other papers published over the last 60 years or so to help develop the case further, but in reality without some better science that seems absent (radio carbon dating, DNA analysis to show familial relationships of remains, and so on), it might be hard to get it over the line from "seems very likely to be the best explanation given what we know today" into "almost impossible to be explained any other way".