Both sides are partly right, and which one wins depends on the decision the report feeds. If you're deciding where to spend content budget, strip brand out. Most brand demand comes from TV, word of mouth and paid, so rising brand clicks will make whatever SEO did last quarter look better than it was. If you're reporting to someone who only looks at sessions, keep branded traffic in, but show the split as its own line so nobody mixes the two up.
I'd stay away from brand share as a KPI, though. It moves when competitors spend, not when you change something on the site. Honestly, how do you all split it?