i apologies because of answered to fast. I misunderstood that you had already fixed it without closing the note.
I use to use access=private for this kind of access but your version is also correct. To me, access=no is when the access is totaly forbidden (closed road due to a damage for example) but i realize that wiki says "access=no tag indicates that the object is not to be used by the general public"... So why not.
Are you ok to close this note ? Given that you resolved it :-)