(a) Notwithstanding Section 1120, only the following noncommercial vessels that use pilotage services are exempt from the pilotage fees and surcharges established pursuant to this division, except for the board operations surcharge as established and calculated pursuant to Section 1159.1:

1. (1) Maritime academy training vessels, whether foreign or domestic.
2. (2) Vessels owned and operated by a nonprofit museum or foundation.