Originally Posted by Qtip

I disagree. The PIC is the one signing the release (if used) or logbook, or both (if a release is used). If the person in the left seat is current and qualified then there is no reason for the Check Airman to be the PIC, hence he/she is assigned the trip as SIC. If the person in the left seat is not qualified, let's say still in IOE or just out of currency of some sort then the Check Airman is the PIC from the right seat while the applicant in the left seat is "acting" as the PIC but listed as SIC on the release.
§ 121.385 Composition of flight crew.

(c) The minimum pilot crew is two pilots and the certificate holder shall designate one pilot as pilot in command and the other second in command.

As far as a Check Airman logging PIC from an observers seat I disagree. The only FAR that may allow a Check Airman to "log" PIC is IAW FAR 121.545 if he/she is actually manipulating the flight controls, but even that's a grey area as this is 121, not 91: In 121 the "sole manipulator rule" of the flight controls can not be used towards a certificate or a rating (PIC can always log PIC, the SIC can always log SIC, regardless of who's the PF or PM/PNF) Can it be logged? Sure, a logbook is a personal document and nothing is illegal to log. What is not legal is to use flight time contrary to the FAR's for currency or using/attempting to use it towards a certificate or a rating.