This is not really a fault as such (AB works perfectly fine), however more of a statement, or perhaps a bug (?)..
I have an intranet (local development) server that runs php 5.6.4 and have a few Wordpress 4.1 dev sites placed on them. Akeeba Backup functions perfectly well (backups perform satisfactorily and DR recovery using the backups works just fine), however the upgrade page for AB doesn't seem to like the PHP version and insists that my php version is incorrect. It subsequently won't let me do automatic upgrades (for example from 1.2.0. to 1.2.1).
Switching off the "Display php warning" in the System Configuration does nothing, the warning still appears.
On my production sites however - which are running php 5.4.30 - all is well, no such php warning is displayed and I can upgrade without any problem whatsoever.
Tried back-revving the version of AB to see if it had any effect - went back as far as 1.0.1, but all exhibit the same php warning in AB, on the php 5.6.4 sites.
I stress that this isn't a problem - backups (and recovery) still perform without issue.