Michelangelo did, in fact, paint, with his own hand, the celing of the sistine chapel. He had a handfull of assistants, not hundreds. Much of their work involved mixing colors and preparing and spreading wet plaster. Fresco painting involves painting onto wet plaster so that the color embeds itself in the drying surface. The celing was painted in sections and each section had to be completed during the plaster's drying process.

Michelangelo drew many sketches of each section before painting and for each section a cartoon was made on paper to be laid over the wet plaster. This was then pierced along it's lines to create an outline in the plaster when the paper was removed.

He did paint while standing. Not only was there no need to build the scaffold so close to the celing, lying on ones back is a very physically restrictive way of painting and would not have been conducive to the time constraints of the work.

It wasn't even the work he wanted to be doing: He saw himself primarily as a sculptor and was far more interested in completing a group of sculptures for the tomb of Pope Julius II. Four years of painting like this, living in cramped quarters where he had to share a bed with his assistant, all the while fighting over money with the Pope and writing home to his family about the suffering and turmoil of his existence. Only to have your classmate steal his glory :(

Source: Ross King - Michelangelo and the Pope's Celing