Every major retailer has the same repair route for printers - the customer calls the manufacturer direct. This is a better system than having to go to the store. Yes, the Sale of Goods Act makes the seller responsible, but to claim on the manufacturer's warranty on printers or monitors you go to the manufacturer. THEY provide the service, direct to the customer. The store was acting as any retailer would do in that situation. The manufacturer will REPLACE the printer and not REPAIR it, all on-site. So you get a better service as you do not wait for a repair.
I cannot comment on the warranty invalidation, I know Epson will not fix a printer that has had refills/compatibles where they are aware of it. I'm not sure what Lexmark's stance is with this, but again if you contacted them direct you would know.
In compliance with the SoG, the store should have offered to contact the manufacturer while you were there, to arrange a convenient time for Lexmark to pick up the printer and replace it (they do not fix them).