The DMG reference is incidental.
It comes up on p. 37 -- "(and it is best to use 1 actual day = 1 game day where no play is happening)" -- in a section that highlights by example why keeping track of "when" different adventuring parties are is important.
Some penalty must accrue to the non-active, but on the other hand, the over-active cannot be given the world on a silver platter. ...Being aware of the time differences between groups of player characters will enable you to prevent the BIG problems. You will know when the adventuring of one such group has gone far enough ahead in game time to call a halt. This is particularly true with regard to town/dungeon adventures.
On the following page:
In effect, the key is the relative import of the player characters' actions in the time frame. Generally, time passes day-for-day, or turn for X number of real minutes during active play. Players who choose to remove their characters from the center of dungeon activity will find that "a lot has happened while they were away", as adventures in the wilderness certainly use up game days with rapidity, while the shorter time scale of dungeon adventuring allows many game sessions during a month or two of game time.
If something "makes so little sense as to be utterly ridiculous," then one just might be misinterpreting it. It is unlikely that Mr. Gygax intended to be ridiculous, and he was writing from extensive experience as a DM.
Although it may be preferable not to end a session with characters in a dungeon, it is indeed silly to assume that they spend a day or more standing (say) before a door, ready to open it. Common sense (upon the reader's stock of which Gygax often relies) suggests picking up the action in that part of the campaign just where it left off.