I was aware of Fischer's opinion a long time ago and, in fact, I knew about Staunton before Bobby Fischer ever mentioned him. But, here's a little secret: until yesterday I had NEVER played over a Staunton game.
Apparently Fischer had a higher opinion of Staunton's play than some of his contemporaries. Thomas Beeby didn't like Staunton, claiming after he beat a couple of players Staunton gushed 'offensive flattery' because his real objective was to inflate himself. On the other hand, when he lost it was never because of his lack of skill but rather because of carelessness, inattention, fatigue or he got bored during the game or some such. Beeby claimed Staunton was so eaten up by self-conceit and his opinion of himself so exaggerated he could not be a safe guide as to the real ability f other players.
From 1840 onwards he became a leading chess commentator, and won matches against top players of the 1840s. In 1847 he entered a career as a Shakespearean scholar. Ill health and his two writing careers led him to give up competitive chess after 1851. In 1858 attempts were made to organize a match between Staunton and Morphy, but they failed. It is often alleged that Staunton deliberately misled Morphy while trying to avoid the match, but some claimed he was simply afraid to play Morphy. Come to think of it, maybe Staunton and Fischer were kindred spirits and that's why Fischer liked Staunton so much.
I think Fischer lost a lot of skill in a hurry after he became world champion. His second match against Spassky for the "world championship" was a joke and nobody was really too interested in the games. By the way, I did a review on the fascinating book on this match by Nenad Nesh Stankovic HERE. I have to tell you, Mr. Stankovic handled Fischer better than I would have because even if I was being paid to babysit him, I could not have stomached Fischer's antics.
I remember hearing one of Fischer's absolutely insane radio rants where he claimed the games from the first Karpov-Kasparov match were made up with the help of a computer because they played so well. Fischer simply did not understand the games...proof that in his absence chess had simply advanced to the point he didn't understand the games of the two best players in the world. That's why he tried to level the field by inventing a new version of the game.
Back to Staunton...unlike most players of the day, he was not an all-out attacking player but he was known for accurate attacks when his preparations were complete. Here's one of his games I played through.