What rules allow a student pilot to add oil to an airplane?
The FAA doesn't consider adding oil to be maintenance. The Hochberg (2016) interpretation says:

The subject of adding oil is often debated; however, we note that it
is not an item included in part 43, appendix A, paragraph (c), which
lists items the FAA considers to be preventive maintenance.

Also see the FAA's Flight Standards Information Management System, under Elements of Maintenance (emphasis mine):

In broad terms, it has been generally upheld that basic servicing
tasks, such as fueling and adding oil, are neither maintenance nor
preventive maintenance. But even that has some caveats. When adding
oil requires a precise sequence of steps or partial disassembly to
gain access, then that would be considered a maintenance activity.
Adding oil to an oleo strut for example, would be a maintenance
activity, whereas adding a quart of oil to a GA aircraft would not.

Since adding oil isn't maintenance - at least not in a simple GA aircraft - part 43 is irrelevant and there's no requirement to have any type of certificate to be allowed to add it.