Yep, that's actually one of the common mistakes people make with low carbing. Fats and oils have just had such "bad press" for so long that many people automatically think of replacing the carbs with protein, because fats are so reviled.
Excess protein is converted to glucose by your liver, so it can act somewhat like more slowly absorbed carbs to the diabetic. While replacing carbs with protein might be ok to a limited extent, it's really not the preferred option for many of us.
Additionally, as you point out with your nephropathy reference, too much protein can really be hard on your kidneys. The reason for this is that, in order to convert protein into glucose your liver has to cleave off the amine group from the amino acids. These molecules form nitrogen compounds (kind of like ammonia) that your kidneys then have to mop up.
Of course our kidneys are designed to do this job and with moderate protein intake it is no real problem. But you're correct that you can indeed have too much. The bottom line is that dietary fats aren't nearly such a bad thing as we have been led to believe, and replacing some of our carbs with fats can be really beneficial for diabetic BG control.