In at least some models, setting this flag results in some meshes having very incorrect position/rotation.
Eg:
AI_CONFIG_IMPORT_FBX_PRESERVE_PIVOTS=true:

AI_CONFIG_IMPORT_FBX_PRESERVE_PIVOTS=false:

I'll try to create a smaller example model, this one is quite large and isn't public.
I see this too, but I don't have an exact model to check.
I had same problem, test this model: https://www.syncs.online/W7z/BMW_i8_Coupe_2015_3D_Model.zip
AI_CONFIG_IMPORT_FBX_PRESERVE_PIVOTS=true:

AI_CONFIG_IMPORT_FBX_PRESERVE_PIVOTS=false:

+1, seems to have been an issue for a while (over a year)
We are working on fixing this as we really need this in Godot.
@RevoluPowered Just wanted to see how you were getting on with your fix for this issue?
Most helpful comment
We are working on fixing this as we really need this in Godot.