Got an idea this is a point of law rather than specific to BMW...or so I have been told.
I have got an alternative idea.
That this (an extended warranty) is an insurance backed product. The underwriters of which may have stipulated that, in order to insure the risk, they want the service work conducted by the original manufacturer. This might make sense as the extended warranty may have been sold by BuMW, who are keen to do the servicing, even though the risk (the insurance part) is actually insured by someone else. It may also make sense as it may ensure the work is done correctly, not be carried by matey with a lump hammer.
A possible example of the brand holder dictating terms to an insurer can perhaps be seen in NIG's refusal to insure motorbikes under their BuMW Motorrad policy going to Morocco, unless they are on a BuMW organised trip.
It would be little different to an underwriter stipulating that, in order to insure my motorcycle in central London, they require the vehicle to be garaged (at my home) if it is within half a mile of my house. There is no law that says I have to garage my motorcycle but an insurer can request that I do, in order to insure me at all.
Anyway it's all assumption. The extended warranty's policy's Terms and Conditions will hold the answer, for sure. It's quite possible that they make no stipulation at all. The original poster hasn't told us what they say, making his question difficult to answer. Instead his information is limited to the not uncommon: "I think I read on here somewhere ...." - The basted son of, "I think a mate once told me....".
Here, being UKGSer, where I
certainly read that it's definitely a good idea to check the oil using any method, other than that stipulated in BuMW's carefully crafted Owner's manual.