In my case, it was purely because of my hosting machine running PHP 4.4.0 and the eZ 3.6x install wizard told me "with bold letters" to use 3.7 instead when it detected php4.4. I cannot downgrade PHP because of other services running on the host that need php4.4.
I could offcourse run it in it's own chroot/jail-environment or something, but I do not want the pain of doing that with apache (especially),postgres and php together.
I think it's possible to run multiple versions of PHP on a single apache server. I have seen this with php 4.3 and php 5.0. But I don't know if this is possible with version 4.3 and 4.4!