This is one of the more controversial topics in Hungary.
You need a little historical background: as you might know, Hungary was under Soviet occupation between 1945 and 1989 and had this system which is usually called socialism. In this era Hungarian gastronomy was destroyed, anything but the most basic ingredients were impossible to get (perhaps this changed by the end but it doesn't matter for our story) so most Hungarians had no idea what good food is. If you understand Hungarian, read István Váncsa's article from 1979 where he is making a not even particularly fancy meal and describes a) what ingredients are not available b) why he needs to do it at home as the restaurants at the time served nothing worthy of a restaurant. Let me add: they were called "hospitality industry units" with an emphasis on industry. There was one cookbook to be used and boy, did they use it. However, everyone grew up eating this gruel and it's familiar to them so when you call it inedible crap they tend to get offended a bit. (Let's not even mention the deluded people who have nostalgia towards the whole era.)
Most restaurants haven't recovered until the 2010s and still there are a lot of places which serve this horrible fare (what the Ramada Balatonalmadi dared to serve as lunch just this month wouldn't been out of place thirty years ago). Right now there's something of a gastronomy revolution sweeping the country where the new craze among the newly rich is flaunting their wealth by funding good restaurants and attracting good chefs. It's practically impossible to have an up-to-date "good places" list. http://www.gaultmillau.hu/ettermek is one of the reliable lists.
So Mark Mayo's list is not bad. But the Balaton pike-perch (fogas)? Sure, world famous fish for centuries. But when was the last time anyone has seen that in a restaurant? 1942 or so, probably. Certainly not in the last fifty years (first some pesticide overused washed into the Balaton in the sixties then non-native fish were released which didn't help). The last few years commercial fishing is banned on the Balaton anyways.
Also, the halászlé is not Hungarian, it came to Hungary from Serbia and actually some of the best could be found in Serbia close to the Hungarian border: Čarda Pikec in Bezdan. Nonetheless, halászlé became popular in Hungary in the last hundred or so years but again, be very careful where you eat it because a typically restaurant will use very low quality fish as they hope the strong peppers will cover the taste (this also explains the popularity -- it is possibly to make it on the cheap).