As you already noticed jBPM 5.3 comes with JBoss AS 7.0.2 and it does that for some reason - AS 7.1.x was not completely tested with it so some issues can arise while running on it. It should provide main capabilities meaning being able to execute processes on it. Some components around the core like reporting could (and apparently do) experience some problems.
jBPM is in general application server agnostic so you could run it on whatever container you like but does not mean that it will be certified for all of them. Many community users run it on Tomcat or other app servers and it is always welcome to contribute back in any way - blogs, wiki articles, etc.
Currently there is some work around supporting AS 7.1.x and best way is to report problems with test case/steps to reproduce in jira like it is done for reporting problem.
Do you have any issues executing processes on AS 7.1.x or only with reporting?
Cheers
P.S.
Please don't post same questions on many threads it makes it difficult to keep track of open questions if they are duplicated.