Hmmm... you maybe be right in theory , but let me give you some inside information about BMW cars and how garages operate before you think about further giving advise.
How much do your garage charge you for changing transmission oil?
A typical BMW automatic transmission uses a minimum of 7~10litres of transmission fluid, you can buy genuine BMW ATF at the cheapest around $150/L and the cheapest BMW OEM transmission filter cost more than $200 and are china made, plus you need to replace the transmission oil pan gasket if you change the internal filter within the transmission ...
So you might tell me that your garage charge you $2000 to CHANGE your transmission fluid???
The normal practice is to just drain about 5 litres of transmission fluid and REFILL with 5 Litres of new fluid and charge you $1000, because the garage KNOWS that you don't need to change the fluid just need top up...
Do your maths, no garage will have enough confidence to fully replace ATF on a BMW and even if you are willing to pay $2000 for parts plus labour and they risk damaging your transmission or cause a oil leak?...
E46 transmission oil should be longlife fluid... Don't need replacement for at least 100,000km, just need top up... Don't be fooled by "Garages"... This is how they make money...
By the way... When you go to BMW service center, ask the SA about your car's problem BEFORE they open the repair order, they can give you a good quote before checking your car...