When I was in fifth grade, just learning trombone, one of my friends, who was learning clarinet, asked me how I could play trombone. Doesn’t it go up into my mouth? I had to take the slide apart to show him how it looked.
Some time after that, I started to hear jokes about some hayseed who watched a trombonist intently, and then declared to one and all, “He don’t really swaller that thing.”
Since I actually knew someone who thought I did, I guess it should be no surprise how long the confusion has been around. For those who don’t mind jokes “as old as the hills and twice as dusty:”
And when one of his companions demaunded him what kind of Musicke did please him best of all he heard there [in Venice], hee saide: “All were good, yet among the rest I saw one blow on a straunge Trumpet, which at every push thrust it into his throate more than two handfull, and then by and by drew it out againe, and thrust it in a fresh, that you never saw such a greater wonder!”
Then they all laughed, understanding the fond imagination of him that thought the blower thrust into his throat that part of ye Shagbut that is hid in putting it back againe.
Source: Baldassare Castiglione. The Book of the Courtier (1528), translated from the Italian in 1561.
(Sackbut, in various spellings, was the sixteenth-century English equivalent of the original Italian word trombone.)