it wasn't a broken tail light stop, they were stopped because they matched the description of suspects in an earlier armed robbery
Edit - Here's a Snopes link describing the particulars of the falsehood: http://www.snopes.com/philando-castile-was-not-wanted-for-ar...
"Police who pulled over and killed Philando Castile reported they thought he might have resembled a suspect in an armed robbery case."
He was not stopped over a broken light, police _thought_ he could be armed and dangerous. (I can not judge the validity of their suspicions)
From all accounts so far the officer radioed he had a broad nose.