How can you think that they are NOT separate?
Your proper weighting has no dependence on your buoyancy skills or what orientation your body is in.
Your buoyancy can be neutral, no matter what weighting you have (as long as it's at least enough). And it certainly does not depend on what orientation your body is in.
Your trim (the orientation of your body in the water) can be perfectly flat/horizontal/sky diver position, even if you are totally over weighted and even if you are going up and down like a yoyo.
So how do you teach your new OW students the relationship between weighting, buoyancy, and trim? How do you teach proper weighting if you don't teach buoyancy control and proper trim? And how do you teach buoyancy control without proper weighting so that students are not struggling to not yoyo and get horizontal? What is your method for getting them neutral and in trim by the end of the first or second session on scuba? I describe mine in my first book.
For new OW divers proper weighting is critical to teach them good buoyancy control and trim so they are not fighting to achieve it.
For experienced divers one can possibly get in trim while being overweighted but it takes some work. Posture, body composition, type of BC, buoyancy characteristics of other gear carried, etc., can make it a real challenge. I have always taught that buoyancy and trim are tightly connected.
Starting with not only the proper amount of lead but the placement of it depending on the person. Trim is not easy for some people to achieve without putting the lead where it needs to be when they first start learning.
Some people with more body fat need the lead to be lower or higher on the body when in a horizontal position to be able to get into good trim without fighting for it.
Getting in trim also very much depends on the the way any air is distributed in the BC and if using a drysuit the issues are compounded.
Yes you can be neutral while overweighted but that necessitates a larger volume of air that is going to shift when you get horizontal. Being properly weighted gives the diver a better chance of managing any issues if less air is required to remain neutral so neutral buoyancy and trim are directly connected.
Someone going up and down like a yoyo is more than likely not going to be in trim.
They are either finning to get down with their head down or trying to fin up because they are having problems controlling their buoyancy. Going up and down like a yoyo is indicative of someone who has not grasped the idea of proper weighting and how it affects control and position.
Saying that weighting, buoyancy, and trim are not connected is simply not true.