C doesn't have to be the lowest note in order for that chord to be based around it. It just has to be the root note if I'm not mistaken. To my knowledge, what makes a chord the chord it is, is the notes involved more so. Take a C major chord and replace the low C with an octave higher C, that would still technically be a C major chord because it's got the same notes and interval steps and all that crap. Disclaimer, don't hold me to this as I've never confirmed it, it's just based around my observations which could be wrong as I've never had any formal training. Sorry if I told you nothing that helps you. This just got on my mind.