Can a someone with just a PPL log PIC time on a non-transport commercial flight?
Yes, you can log PIC in an aircraft category and class that you are certified to fly. You can log that time during which you are the sole manipulator of the controls. This is the case even if another crew member (the commercial pilot) is the acting PIC.

See 14 CFR 61.51 (e) for this and other situations allowing logging of PIC. 

Following is the relevant section of 61.51 (e):


  (e) Logging pilot-in-command flight time. (1) A sport, recreational,
  private, commercial, or airline transport pilot may log pilot in
  command flight time for flights-
  
  (i) When the pilot is the sole manipulator of the controls of an
  aircraft for which the pilot is rated, or has sport pilot privileges
  for that category and class of aircraft, if the aircraft class rating
  is appropriate;