From the spec related to vkCmdPipelineBarrier:
If no memory barriers are specified, then the first access scope includes no accesses.
This is noted for both, the first and second access scopes, so if I understand correctly:
(1) A pipeline barrier without a memory barrier causes all subsequent commands to wait in destination stage until all commands before finish the source stage. This is a hard constraint which applies to all commands.
(2) A pipeline barrier with memory barrier eases the sync constraint so only subsequent commands that deal with that memory are wait in destination stage (at the relevant access action) until only preceding commands that deal with that memory finish the source stage (at the relevant access action).
Is it correct?