Log integrity handling on central logsystem

I'm looking for feedback how centralized log solutions handle data
integrity; If you would log directly to a central system, that log is
the only source. So you would miss something to compare against.

-Would you rely on taking checksums of the logs and storing them on
another system?
-How do you protect yourself from the fact that the central logging is
compromised with a still growing logfile?
Would you consider signing each log line? Signing within a text file is
fairly easy, but what about content stored in a database?

My customer is currently looking at Splunk. It seems a great way to go
through the logfiles, but I'm not sure that we can fullfill his
dataintegrity requirements with it. But then again it does not stand in
the way of another solution doing it probable.

Patrick