I had the same issue last year.
http://tropicalfruitforum.com/index.php?topic=38938My Big Jim also only rotted on the side exposed to light, including the fruits that didn't get direct sun, which kind of makes me doubt it's sunburn. I watched it slowly happen and the weather was cool and overcast the entire time. I see too many healthy, fruit filled, sitting in full sun Loquat trees around socal for them to be THAT sensitive to sunlight. What variety is yours? How's your weather been? I can't imagine you've had too many days over 70f in MB this year. I seem to remember it starting after we had a few consecutive days of rain. Has any water been sitting on the fruit? I ended up cutting all the fruit off and it decided not to flower this year, but it does look healthy with a lot of new growth. Good luck
Edit: Looking over that old thread and it looks like Jose Spain might have nailed it with Fusicladium eriobotryae. A fungus dispersed by rain and thrives in wet conditions. At least in my case, I think a rain storm dispersed the fungus to the outer exposed fruit. That might explain why even the fruit out of direct sunlight still looked burned. Google image doesn't have the best photos, but you can read the abstract here
http://www.actahort.org/members/showpdf?booknrarnr=1092_46I had hoped a good trimming would be enough, but I think I'm gonna have to spray my tree