No, do not think this way, it is not that simple. Different buildings will have different grounds, do not link them up over copper. Even a shed in your back yard off the same circuit breaker can be different enough to cause issues with sensitive equipment - seen it before. Ethernet interface circuits definitely fall under the sensitive equipment category; lighting, heaters or DC warts for remote devices do not.All the buildings are adjoining, well under 200 feet apart, and on the same block, so the power ideally should also be sourced from the same sub-station, and well grounded (electrically).
"Ground is ground" can lead to problems. At the college I used to work at, they wanted to build a secondary TV studio in another building and link it via coax to the main studio / building a block away. This was in the 1980's, so it was coax, not fiber.Some people over think the "different grounds". Ground is ground. It is the stuff outside your building. How well your electrical ground is connected to earth is a subject for debate. Gigabit ethernet is differential. It doesn't care about ground / earth / anything. It is the difference between the two wires that matters. The standard requires equipment to be able to withstand a bunch of volts between the signal carrying wires and earth.