How are integrated dishwasher's dimensions measured?
I only have experience with two dishwashers (the 10 year old one I replaced 3 years ago and the new one). When I was shopping all standard dishwashers had approximately the same dimensions (plus or minus 1" or 2cm; the dishwashers were sold in the US market), so perhaps the one you're replacing was on the small side. I had to go look at a lot of places to find a dishwasher that would fit (in my case the width wasn't the problem...we put new tile in and most dishwashers were too tall to fit). I don't think a difference of 1cm is enough to consider it oddly shaped; the "specialty" dishwashers (for condos and small kitchens) seemed to have size differences of up to 10cm or more.

As far as the stated dimensions go, they seemed to be very accurate. The knew the one I purchased would be a tight fit and it definitely was (I had to remove the feet on the bottom to fit in in the cabinet). You may want to download the manual/install guides for various dishwashers that you're considering. Usually the top and sides of the tubs are covered with insulation which can be compressed a little as you're fitting it into the cabinet (although you must be careful of any hoses/wires on the sides). The widest part is usually the front part of the tub which flares out to seal with the door.

In my kitchen, the cabinet face and counter top covered a slightly wider/taller hole inside the cabinet. If your layout is the same you may be able shave a few mm off of each side of the cabinet to make it fit.