I've been told, and have read - but don't know this for certain - that there is up to a 3% variation, from manufacturer to manufacturer, within each size. That's why I used the word "about" when describing your tire size in my 1st reply. The 13.1" sidewall to sidewall width falls within that 3% tolerance, relative to 12.8" and only extends the outer sidewall of the tire by .15" compared to a 12.8" tire. Mouse nuts.
The graphic below gives you an idea of the different elements that can be measured. The 13.5" from MT can only refer to the overall width. The overall width of you current tires is also wider than your current sidewall to sidewall width, so don't worry too much about it; it's relative.
The 12.8" or 13.1" or 325mm measures the sidewall to sidewall width, aka section width in the graphic below.
BTW, the section width of the tire on your car could be different than stated by MT if your rims are a different width than the measuring rim. I checked the MT chart and the measuring rim they used was 10". Don't worry too much about that. I just tossed it in to get you even more confused.
Bottom line: if you had clearance for the 12.8" tire, you have clearance for the 13.1"/13.5" tire.