All 5 BMWs I've owned had plastic jacking points under the sill area [*]. I would not use a stand under any other part of the structure than a specified point.
So once that jacking point is in use with the jack, then would you put a stand elsewhere ?
I agree that on the many cars I have seen, the jacking point is a reinforced vertical part of the sill and it may be possible to utilise an axle stand with a wooden block at another point [**], but with axle stands, there is some movement in the telescoping part that introduces instability IME.
With my frame, there is zero instability. I always give the raised vehicle a good shake before getting underneath.
As an aside, I recently (a year or two ago) saw a car on an MOT test having the front suspension checked for excessive play by an hydraulically powered plate moving horizontally to and fro (transversely) under the nearside front wheel. The car was five feet in the air and the whole structure (lift and car) were rocking. You would not have got me under there...
I once bought the inflatable bag from Draper that used exhaust gasses to inflate the bag to lift a vehicle. The first time I used it, the bag was just over half inflated when it burst.
The bag split near the seam on the side. Luckily I was not underneath at the time, but I was close enough that the sill finisher caught me a glancing blow to the forehead. It went with an enormous bang. I had to change my trousers.
[*] Two of the Audis I owned had rubber pads not on the sill for lifting, but the dealers used the sills.... [**] I have done this too many times to count, but not any more since the footwell hole incident.David