If you start a hike in SEKI, you do not need an exit permit (aka endorsement) over Whitney. The "Cross Country Exiting Mt Whitney" permit is only for trips that originate at Inyo NF trailheads. A SEKI permit is good for your whole trip (I know...I got one last year and confirmed at the time.)
http://www.fs.usda.gov/detail/inyo/passes-permits/recreation/?cid=stelprdb5150055 The problem is, because he is a "day hiker" from SEKI's perspective, they probably won't issue him a permit. So he has nothing to show the Inyo folks when he crosses Trail Crest.
