Baseball at its heart is a simple game. On offense you hit the ball, touch the bases and score runs. On defense you try to prevent the running of bases. Key in all of this is actually touching the bases. It is a necessary condition of the game – even on base awards.
Rule 5.06 (b)(4)(I) Comment (Rule 7.05(i) Comment in old format)
The fact a runner is awarded a base or bases without liability to be put out does not relieve him of the responsibility to touch the base he is awarded and all intervening bases. For example: batter hits a ground ball which an infielder throws into the stands but the batter-runner missed first base. He may be called out on appeal or missing first base after the ball is put in play even though he was “awarded” second base.
Yes, this applies even to home runs. Here was an interesting play over the weekend:

Batter hits a homer and then is ruled to have missed home plate on appeal. The Brewers had the play reviewed where it was ultimately decided home plate was touched.
Of interest to me was how the original appeal had to take place. The Giants manager came out and (I am guessing) asked to have the touch of home plate reviewed. It looks like the umpires told him he had to formally appeal first.
This makes sense. A call cannot be reviewed if a call had not been made. The Giants appeal was granted. That meant the Brewers had to challenge whether the base was touched.
Can you imagine how bad the batter would have felt if he lost a homer on a stupid mistake?
According to this awesome page at Retrosheet, this would have been the first lost HR due to a missed base since 1983!
Page 9 of RuleGraphics covers advancing and touching bases.