The coat does appear to have been dyed. It's sort of blotchy up-close. Maybe it was dyed from neutral/white to brown and the brown dye has got uneven over time and gotten bluish. Because up close it does have what appears to be bluish remnants around the stitching and in the folds.
Personally, I like the blue because it does look blue some of the time onscreen and yes, because of Kenner. If it looked brown onscreen the whole time, I'd call it a Kenner mistake that had to be rectified, but that's not the case.
The brown makes more sense because all the other Hoth outfits have a brown/beige color scheme, but I guess you could argue the blue sets Han apart so could have been a choice. To me, it's like the ATAT driver helmet/armor - it's been definitively proven to be light/medium grey, but it looks white onscreen so that's the way I want an ATAT driver fig to be.