How the applicant chooses to log a LPC/LST pass is up to him. It should indeed be recorded as PIC/US if successful, but a FE has no power to insist that it is so recorded.
I've just been told by the examiner who signed off my SEP revalidation that I "should" have logged various check rides (due to being out of club currency,
not LPCs) as P1/S, not PU/T as I had done. But I'm going to carry on doing it my way - it's my log book, and I want the "in command" total to represent the time I didn't have someone else to hand over to if it went pear-shaped.