We've tried a very similar thing by transferring a Mii over the internet, then attempting to load the Mii and Wii sports to see if we could load the stats as well, but we get the same results as you. It must be in the Wii itself...somewhere that we can't access.

Have you tryed using the same mii? You can transfer miis from wii to wii with the wiimote

All you said was "I'm using the exact same mii name." sorry about the misunderstanding.

Im not sure how many topics have had posts saying if you modify a wii file on the computer the wii will not read it.

When your mii was transferred to your wiimote it is labeled as a transferred mii withe blue pants you cant edit it so your wii sees it as a friends mii and not your own. So your wii may not have the stats of the mii. You can try to change the wii id code of your mii to yours. I've done it with mine( gold pants special mii now hahahahah ) but didn't try it with save data don't no if it will work or not but here's how.

Getting a blue-tooth adapter to sink your wiimote to your computer. Now the software.
Go to Google and search for mii transfer software for (place os here). After you do that make a file some ware on your computer and save the mii to the file from what ever slot you put it in like slot 1 to 10.
Now Google mii edit there's a nice little app that is java based and you can up lode your mii to the app. But first make a mii on your wii so to get the wii code from it and wright it down. now upload your mii from your friends wii you tranferd to your wii and change the code of the mii to your wii id. Now save to your file of chose it will save as miibinary.mii
now save it on your wiimote and transfer it to your wii. vala its your mii again now you can edit and what not.