There are two important caveats to the "it's both" claim.
The first is that Lapua or Eley (or other ammo-specific) chambers are only found on custom barrels with specific chambers. Anyone who wants a Lapua or Eley friendly chamber needs to get a custom barrel and have the barrel manufacturer cut that chamber. They aren't available on factory-made rifles.
To elaborate, factory rifles will have a chamber that is made to CIP dimensions or SAAMI dimensions. Chambers on CIP-specification rifles will have chambers no smaller than the minimum dimensions permitted under law. That includes rifles from manufacturers such as Anschutz, Walther, FWB, Bergara, CZ, Tikka, Sako. The length may be longer or shorter on different rifles, but they can't be any shorter than what CIP specs require. CIP specs call for a 5 degree leade and so, too, do SAAMI specs for both Match and Sporting chambers.
The reason why most firearms makers don't put ammo-specific chambers in their rifles is so that shooters can use a variety of match ammos. Even Vudoo, which uses a Lapua-friendly chamber on the V22 custom barrels, says the Ravage V22 chamber is "compatible with the higher quality 22LR Match ammunition". In short, almost anyone with a factory barrel/chamber will find it difficult to see any chamber-based benefit to choosing ammo based on the manufacturer.
The second is that even with a Lapua or Eley specific chamber it's still necessary to test lots of the make of ammo for which the chamber is designed. The use of an ammo-specific chamber doesn't mean that all lots of ammo produced by a certain ammo maker will shoot equally well. No manufacturer promises that a certain chamber will make lot testing unnecessary if only the chamber specific "brand" of ammo is used. It also doesn't preclude Eley from shooting well in a Lapua-friendly chamber or vice versa.
Invariably, the choice of which chamber to use is for many very serious BR shooters based on which ammo maker has the reputation at a given time for producing the best ammo. There was a time, for example, that Eley regularly produced ammo that shot better than Lapua and so the super serious BR shooters who were looking for a new barrel would usually prefer an Eley-friendly chamber. In more recent years, Lapua ammo has improved its reputation at the expense of Eley and so Lapua-friendly chambers, like the Nevius, are favoured.