I don't think I've been paying much attention to this debate recently. It took my Dad to e-mail me the question about the highest point of earth to wake me up to this. Yes, Everest wins the prize for being the highest mountain above sea level but it's not necessarily the furthest point from the centre of the earth. That prize goes to Mount Chimorazo in Ecuador. But it's only down to a geoidal bulge and, as this article points out, it isn't even the highest mountain in the Andes.
At the end of the day, it's not how you measure something, but what you measure it against that matters. The highest point of the earth can vary depending on how you define 'height'. It's like someone asking where the coastline is. Well, it depends if you own the foreshore, want a picnic, are interested in coastal erosion, have fishing rights, want to dump and dredge or whatever - the person and the question are often inextricably linked.