The Wikipedia article is wrong. I read a C on the page with a B flat clarinet and play a C (fingering T 12-- ----). It's simply a convention that most orchestral and band players read the music differently and finger that note T 123- ---- to produce a B flat; nothing in the structure of the instrument requires it.

If they had said A transposing instrument is a musical instrument for which written notes are by convention read at a pitch different from the corresponding concert pitch, that would have been right.