What are the dimensions of the current fridge?

You need to look for a counter-depth refrigerator that is narrower than the usual 36" they come in. There are definitely some out there, but you'll need to measure your width and height limitations.
http://www.homeclick.com/summit-ff71-48-cu-ft-2-door-counter-depth-top-freezer-refrigerator-with-frost-free/p-373477.aspx?chnl=productads&ven=google&kw=FF71&ci_src=17588969&ci_sku=373477FF71&gclid=CIriicOphrYCFYtU4AodqBsAvQ

Sorry now that I'm looking closer to the kitchen I'm wondering how it will look when the fridge is recessed and the counter is sticking out further than it? Hmmm....that's a tough one.

There is a chance to use fully integrated models. LIEBHERR and FAGOR has fully integrated fridges but you would need a cabinet for it.
There is also a freestanding LIEBHERR with a depht of 24 13/16 inch available http://www.liebherr.us/HGH/en-GB/products_us-hg.wfw/id-582409-0_25090-4
Or a freestanding FAGOR with a depht of 24 inch http://www.fagoramerica.com/appliances/refrigerators/torre_stainless_steel.
BUT these models are higher.

Fisher & Paykal and Samsung make the only 33 inch wide counter depth refridgerators. I agree it's a little strange with the couter sticking out, but I think it would be better than what you have now obstructing the doorway.