On an Epson printer, it is Epson who make the rules so, Epson is the final arbiter.
However, independent ink makers are very careful to formulate and produce their ink to the highest standards and it is unlikely that the ink itself would cause a problem.
A supplier like Choice will replace a printer if it can be definitively shown that their ink was the cause of any problems with a printer. By making this claim, it indicates that they are confident in their product.
Almost all problems with the ink side of printers are caused by neglect on the part of the owner. Allowing the printheads to dry out is the most common problem which can be of greater significance with Epson models as the printhead is an intrinsic part of the whole printer, rather than a replaceable item as with many other brands.