BlueMax 23

I had a flat on the drivers side, front tire this week-end. I pulled the spare and saw it was a 17 rather than a 20 inch tireI thought it would be okay and with some reservation I mounted it and headed home. About 15 miles into a 20 mile trip home in the dark I realized there was smoke boiling out from the undercarriage. Long story short, the differential is now toast and has to be rebuilt. The question is - is this because of using the smaller spare tire or was it just a coincidence?