Of all the RE's we've sold, no oil burned that we are aware of. In the BMW world, on a new bike, .5L per 1k is acceptable until it runs in. (on our boxer twin)
20-50 full synth after the first change. Not a drop used in 2200 miles.
Precious needs ca. 0,1-0,2 litres per 1000 km. I doubt that she burns it - the only spot to loose this amount would be the drive pinion´s shaft, as it is surrounded by a brownish sauce that - I suspect - is not only chain grease but some engine oil, too. Hard to say. Does anyone changed the o-ring there? How complicated could that be?
Any warranty left?
To isolate the chain sludge I would thoroughly clean the chain and switch to chain wax for a while. If you still have sludge it could be the seal. Another solution is a dye that you put in the oil. It will show that engine oil is lubing your chain. It has been decades since I used it but I'm sure they still make the dye.