Geisser-Greenhouse Correction Nonsignificant Effect

#1
I've read several pieces of documentation that say that the Geisser-Greenhouse correction for sphericity always increases the p value.

I've noticed in SPSS that if a test is not significant (before any correction), sometimes the Geisser-Greenhouse corrected value is actually less than the uncorrected. For example, take a repeated measures ANOVA with three groups F(2,18) = .211, p = .812. Applying a Geisser-Greenhouse epsilon of .651 gives F(1.303, 11.723) = .211, p = .718

Does this only happen in cases when F is not significant? Is it customary to report the corrected or uncorrected value in these cases?

Thanks in advance!