Can my mother use her primary care doctor while she is in the nursing home here in Oregon?

There are periodic health assessments that must be done by an MD (or NP/PA who works with that MD). Required for reimbursement, and for licensing regulations on Medicare Medicaid and state levels.
If her PCP is willing to go see her at the nursing home to do these, it could work. When small problems arise, the nursing home may send her out to the ER, if her PCP can't see her within 24 hours.
Many 'house MDs" are not necessarily terrific, but have NPs/PAs who work for them that are. In my area there is a good sized medical group that specializes in nursing home care, so they know all the regs, and have staff to see patients whenever needed.
Pros and cons to both choices.

Even if you don't use her PCP, it's nice that you have that option.

At the second best rated hospital in the country, once a patient is a resident of the NH, their regular PCP discontinues care for them, unless the PCP is also on the NH staff.

It is described as "Not stepping on the toes" of the house Doc. Now if the patient is discharged from the NH, then he/she could see their regular PCP again, but why would they?

Using the in house doctor makes collaboration and communication between staff and doc much more efficient.

Maybe, but if they have an in-house doctor, that'd work a whole lot better. Hauling her to doctor appointments is not only inconvenient, eventually it'll be impossible, and you want her to have an established relationship with the in-house doctor sooner than later.