Does their website list a .'mini refrigerator' as a room feature? Uness they dsclosed the fee in advance, or at check in, Id refuse to pay it. Tell them to either bring up a fridge for your use as promised or waive the fee. (A mini-refrigerator is listed as an 'amenity'... they ADDITIONALLY list a mini bar "for a fee". You want the free fridge....)

They decline, empty it and contest the charge.

I wont let crap like this ruin my stay- allow them to decline the accommodation, then take action to correct their error. Deal with the $$ later.