We also found that if an oversized (larger than stock: 12, 14 etc..) of ANY brand is installed with the battery strap overtightened, it will cause the battery to fail. I spoke directly with Yuasa about this. The guy I spoke with explained that if the battery casing is squeezed, it will cause an internal short. We saw this failure on a number of quads (in one day) and found that on all of them that failed, the strap had been overtightened. By installing spacers between the strap and the tray, the problem was alleviated. Obviously, the stock size battery does not have this issue.
Just one note to clarify what you said. The stock "9" series battery is the exact same size as the "12" series battery. The "14" series battery is slightly larger in height only (about 1/4"). Since the strap holds the battery down, when tightened on the taller batteries it can "squish" the battery causing the examples he is mentioning. I have one of each size Yuasa battery installed in my quads (9 series, 12 series, 14 series), and I have had no issues. BUT I did shim the battery strap higher to accomodate the extra height on the 14 series battery (some OEM battery straps have two rubber isolators glued together instead of one thicker one and you can just remove one layer to do the same thing). One other issue that has been mentioned is that some other brand batteries have a slightly larger case size, even though they are replacement batteries for the numbers above. A few years back, one guy got pretty upset when he swore that an off brand battery he bought would not fit in the battery tray, and everyone on the site swore it did. I think a razor knife around the edges of the battery box opening fixed the problem.
Also, don't forget that worn out components (battery tray and strap isolators) can wear out and cause a loose fit, having a similar short out problem due the extra vibration.