From your description, the pilot was doing what is normal for getting a container ship to the Port of Oakland.
The outbound lane, the one North of Alcatraz is the deeper of the inbound and outbound lanes. Therefore deeper draft
vessels that are inbound sometimes take the outbound lane because of this. The Maersk ship was probably drawing a lot of water
or there was a another ship in the inbound lane and the pilots agreed to do it this way.
The reason you saw the ship turn hard to the right is because they must get around Harding rock and start making their turn for the Precautionary Area. Besides, if they don't turn hard after rounding Harding they will soon be out of deep water
and hit bottom.
Its always best to sail outside of the shipping
lanes but if you must cross a lane then try to visualize where the lanes are so you can anticipate hard turns that the ships will need to make.
The area on the East side of Alcatraz is the Precautionary Area and is basically an intersection of the shipping
lanes. Sailing in there can be very hazardous. Take a look at chart 18650. It will show you where the shipping lanes are in the central SF Bay
The Port Captain
has deemed that all ships in the SF Bay
have the right of way because they are very limited in where they can go...mostly because of their draft
and limited maneuverability.