A fuse IS a short - it's supposed to be a short circuit until too much current flows and it melts and becomes an open circuit - forget about the fuse.
If an earth leakage breaker trips then the whole house loses power - RCDs and RCBOs usually supply the whole distribution board. If this is happening then current is leaking away and a potentially unsafe condition exists.
If a single pole Miniature Circuit Breaker is tripping (just taking out downstairs power for instance) then too much current is being drawn.
In either case you seem to have diagnosed the cause of the problem - you need to decide if you call in an engineer to repair the machine or just get a new one.
I have owned fridges since 1966 and had never experienced one tripping an RCD. You would be unwise to follow Alan's advice, "try to move circuit to a non rcd breaker." If there really is an Earth Leakage fault in the fridge then taking away the RCD protection might be lethal.
Peccavi
April 2009