Possible to run multiple Reporting Services (SSRS) instances on different machines with databases on same machine?
Yes, you can have several Report Servers installed on a single SQL Server.  As you noted, the multi-instance support on a single machine is available, but not what you are after.

For multiple distinct ReportServers on different servers, but using a single database, you simply have to configure this in the Reporting Services Configuration Manager.  

As noted by GShenanigan this is described in the Scale Out Deployment. http://technet.microsoft.com/en-us/library/ms159114.aspx (same link)

In that phase of installing a Report Server, you must choose the database server that you want to use.  Then you can separately use the RS Configuration Manager to either choose the existing ReportServer datbase or choose a new database named to whatever you want to call it.  

When a new database is set up, the ReportServerTempDB will be named similarly.  For example, creating ReportServerHQ would have a ReportServerHQTempDB also created.