What rule in Part 95E grants this authority to GMRS repeater owners?
As I recall, you don't need any rule at all. A repeater is considered private property, and the FCC has ruled on that many times.
However, there is also this:
95.1705: Individual licensee duties. The holder of an individual license:
(1) Shall determine specifically which individuals, including family members, are allowed to operate (
i.e., exercise operational control over) its GMRS station(s) (
see paragraph (c) of this section);
(2) May allow any person to use (i.e., benefit from the operation of) its GMRS repeater, or alternatively, may limit the use of its GMRS repeater to specific persons;
(3) May disallow the use of its GMRS repeater by specific persons as may be necessary to carry out its responsibilities under this section.
Then there's this interesting section.
(f)
Cooperative use of GMRS stations. GMRS licensees may share the use of their stations with other persons eligible in the GMRS, subject to the conditions and limitations in this paragraph.
(1) The GMRS station to be shared must be individually owned by the licensee, jointly owned by the participants and the licensee, leased individually by the licensee, or leased jointly by the participants and the licensee.
(2) The licensee must maintain access to and control over all stations authorized under its license.
(3) A station may be shared only:
(i) Without charge;
(ii) On a non-profit basis, with contributions to capital and operating expenses including the cost of mobile stations and paging receivers prorated equitably among all participants; or
(iii) On a reciprocal basis,
i.e., use of one licensee's stations for the use of another licensee's stations without charge for either capital or operating expenses.
(4) All sharing arrangements must be conducted in accordance with a written agreement to be kept as part of the station records.
Does 4 apply to repeaters? That's interesting too, specifically with "open" repeaters.