This link is out of date. It only provides the BSA links to Support Matrix PDFs, which stopped with release 8.2.01.
The replacement to the Support Matrix is the SPAC Utility. While this lists supported operating systems for the various installable parts (app server, RSCD agent, etc), it does not list the support database versions.
The BSA 8.5 documentation page for setting up the database claims that its Supported Platforms page will provide those details. However that page never mentions database platforms and only links to the SPAC Utility.
Edit: it turns out the supported database list is provided on the Minimum Software Requirements page of the BSA Documentation.
I just tried this, and the way to get a valid result is rather narrow.
1) I can only see the Database tab by clicking on the first result in the Application Server section (Microsoft Windows -- Server 2008). If I click on any of the other options, I only get the "UI Language" tab. This should apply to all versions of the application server, since each can send a SQL call to any of the supported database types.
2) This only works for BSA 8.5.00. There are no tabs at all for the application server choices in 8.3.03.
3) It's not clear from the start of the SPAC Utility that one would find these values this way. Would it be possible instead to make a separate Component entry for "BMC BladeLogic Server Automation Database"?
Let me check if that can be added.