Arnold Jacobs was against free buzzing (buzzing without a mouthpiece) because:

When the signal is sent from the brain to the lip, it goes to the entire lip, which is not desirable, unless you’re a tuba player. With the mouthpiece in place, the bite of the mouthpiece (where the rim turns down into the cup), isolates the tissue inside the mouthpiece from the rest of the lip so that only the muscle inside the mouthpiece responds to the brain; the rest of the lip does nothing. Because of this, buzzing without a mouthpiece is completely different than buzzing with a mouthpiece. You only have an embouchure when the mouthpiece is on the lips; free buzzing accomplishes little or nothing besides loosening up the lips.

I’ve always thought it interesting that the French refer to both the lip muscles and the mouthpiece by the name “embouchure.” They seem to have understood the importance of the interaction of the mouthpiece and facial muscles even before Jacobs.

Jacobs said that a certain amount of mouthpiece pressure was required on the lips to produce this isolation. A mustache can interfere with the isolation causing missed notes or using too much pressure to try to achieve the isolation. This is why you see many brass players trim their mustache so it doesn’t interfere or even shave the entire top lip.

Supporting Evidence:

Jacobs told me a story about when he was on tour with the Chicago Symphony playing the Mussorgsky-Ravel Pictures at an Exhibition. He said he started having trouble with “Bydlo,” the extremely high tuba solo; he couldn’t figure out why he was having problems, so he started thinking about possible reasons. It dawned on him that he had started growing a mustache while on tour and that might be the cause of the missed pitches. He shaved it off and that immediately eliminated the missed notes.

During one of my lessons with Mr. Jacobs, I told him about a recent event where my lip had gotten very sore from playing too much and that it seriously put an important concert in jeopardy. He told me my moustache was causing me to use too much pressure. I started shaving both lips so that the inside of the rim of the mouthpiece rested on bare skin, although part of the rim rested on mustache hair. That greatly reduced the need for excessive pressure and I have not had the problem since.