I just posted a new thread about this, my search did not turn this thread up at first.
The Bilstein strut and the Sachs OE strut are dimensionally the same. The spring perch is the same. It is not the spring perch. It is not the dimensions of the strut itself.
I compared the OE strut to the Bilstein strut side by side at the BMW dealership. The only significant difference I can see is that the rod on the Bilstein extends out 1-1/2 inches farther than the OE strut. And it takes more force, quite a bit more, to compress it fully. This is on an "OE equivalent" Bilstein, not a performance upgrade unit.
The only explanation I can come up with is similar to what UDM said; the higher internal pressure and the naturally higher at rest position of the Bilstein strut lifts the front of the car. I see someone arguing that the additional upward force is not enough to make the car ride higher, but I disagree. You do not have to lift upward very hard to move the car up. Same goes for the strut.
UDM, let me know how shorter springs work out. I don't want to lower the car below the factory ride height, I just want it back down where it was. 3/8" or so lower would be right.