Your instructor is right.. I was asked the same question during my CFI with the FDSO about loging safty pilot time and both loging pic. You both can log PIC but only the one that LANDS can count the XC time. Remeber that XC time requires a Take off and landing at an airport grater then 50nm for ratings other then the ATP. You both cant count the T/O and landing so you both dont get the XC time. The inspector said she has to throw out hours all the time becuse of this common mistake..