In my department, PhD admissions and funding are two separate processes, which means many PhD students are admitted even if there is no funding for them. To be admitted, an applicant typically needs to impress a faculty member enough to want them to take the applicant on as a student (which means this faculty member becomes the applicant's advisor, if they decide to accept the offer of admission). To get funding, an applicant need to impress at least one of the several faculty members who controls a training grant enough to want them to offer the applicant a slot on the grant. It is very uncommon (if not impossible) for any PhD student to receive funding outside of a training grant via an RA, TA, or other source, at least in the 1st year.
As such, it is fairly common for a professor who wants a particular student to join the department as their advisee to lobby for the student with one of the training grant directors. This is particularly true in cases where the student of interest has communicated that they have a funded offer from a rival department and will likely not consider our department without a similar funding offer being extended.
Because of this practice, a difficult situation sometimes arises when funded students want to switch into a research area that is still within the scope of their training grant but not within the scope of their advisors' interests. Because both areas fall within the goals of their grant, these students are not risking their funding by switching (although they may be risking an additional year of PhD studies, depending on how late they switch). However, because their initial advisors usually had a large role in helping them secure funding, they are hesitant to make the switch out of a feeling of obligation to their advisor (e.g., "Dr. Z did a lot of work recruiting me and helping me get a funded offer, so I feel bad leaving her").
In situations where funding is not directly tied to one's advisor (but may be indirectly tied to them), what obligations does the student have to their advisor? Should the student feel free to switch advisors if they discover that another research area appeals more to them? Are there any special considerations or etiquette protocols?