A couple of subtleties.
Access Web Apps did store their data in tables SQL Azure Databases, one database per AWA. The apps themselves were stored, if that's the right word, on SharePoint. Unlike their predecessor, Access Web Databases, the forms ran only in a browser. Neither supported Reports, a big shortcoming, IMO, but not the only one. Access Data Macros in AWAs were implemented as SQL Azure Triggers and regular macros as stored procs (if I recall that bit correctly) and maybe as functions.
I have to verify, but I do think we had the ability to link to SP lists in A2003. Now, I wonder where I left that A2003 VM....