Well I wonder if that's true.
At an early stage in my relationship with inkjet printers I realised two things:-
1. Anything other than the manufacturers' cartridges may damage the printhead.
2. Manufacturers make the real money from selling cartridges, not printers. That's the way it is.
I've never used compatibles, and I do not recommend it to my clients - I've seen too many printers with wrecked printheads. You've probably got one now, and although it may well be the case that Epson are on slightly thin legal ice over this, they may be on very thick ice, and you would have to take legal action to find out. As far as I'm aware that hasn't happened yet. My 'real world' advice is to fit Epson cartridges and see if that might cure the problem. If it doesn't..........well, the printer has Epson cartridges now, doesn't it?
The alternative is to buy another printer, and this time stick to the correct ink cartridges.