A false reporter is a user who accuses or reports someone on 'false accusitions.' On Hatena, it refers to Flipnotes reported for the wrong reason.
Reasons for reporting
Most FRs report a Flipnote mainly because they're jealous of its popularity or just for the sake of the response and attention. If done on a Flipnote on the Most Popular page, its likely for the sake of bumping another's rank down.
When is it "False Reporting?"
A person who spins off another Flipnote can be legitimately reported when the original creator reports them. A Flipnote does not need to break the rules. Any spin-off can be reported by the previous creator for any reason at all.
It is false reporting when a person whose art style is similar to another's is reported. Reporting for a similar art style cannot be reported. It must be a Original Character by definition, not by originality.