My cabinets are set at basically 68 1/2 inch on one side and 68 3/4 inch high on the other side. Nearly all fridge I am looking at are basically at that exact height for their top cabinet height minus door hinge which won't affect because will not be near the cabinets.
Nearly every manufacture is recommending 1-2 inch top margin for airflow to reduce energy bills and to make fridge last longer.
The width I am allowed is 38 inches so I'll have adequate room on the sides (at least 1-2 inch).
Don't know if you are still looking for an answer. The top airflow is very important. Warm air rises and must have a place to escape, which is mostly at the top air space.
If you ignore the specs, you may risk more than just energy efficiency or longevity. You may be very disappointed when you come back from shopping and the 'frige won't handle the sudden load properly, you spoil some food, and your freezer won't hold zero for the next 24 hours.
Somehow you have to find a way to get the warm air from top of the 'frige space. You only need to find one 'frige short enough. Or move the cabinet up. Or cut your lower rail on the cabinet to meet spec. More risky but less visible, cut four, 2" holes in the top and bottom of the cabinet to vent the hot air. Or put a small, silent computer fan and vent in the cabinet. A lot of work, but I would never ignore the venting specs.