I think it only qualifies as a summit if you're having fun when you do it. This holds true for sit-start summits of The Big R, or speed climbing, or if you're just doing it for the chicks. A lot of people on this board want to make fun of the best climbers, but lets face it...they're having way more fun than you are. You're living your life snaring yourself in arbitrary rule sets.
For the record, I think a true summit would require tagging sea level first. However, if you start at the bottom of Death Valley, and then you summit, is the mountain actually higher? I think this is the more important question.