Why would the Mfg approve someone's else ink when they can make you use their's. Just put in the original ink before calling for warranty. I have less problems with Lyson than Oem and they will warranty if the ink is the problem. Its not like using nitro, its like using Shell or Hess in your car to keep the injectors clean.
Since Mutoh does not actually make ink, it's ink is third party as well.
The ink delivery system, including the head, orings, tubing, etc, is made up of components designed to be compatible with that ink.
Not all inks are made with the same solvent systems and you can certainly put in inks that will damage parts of the ink delivery system. You could mix aqeous inks or full solvent inks and cause problems that would not be warranty. So some inks are like Shell or Hess, but some are like diesel and some like nitro.
Some have particle sizes larger or less colloidal than OEM inks. Which could lead to clogged nozzles and other issues.
None of these would be design or quality problems from the manufacturer and be liable for warranty repair or replacement.
Some 3rd parties guarantee their inks and pick up that part of the warranty.