It is clearly both. That is precisely what the "HCT" series is - all that series are by definition, level shifters. So if you had used 74HCT595s, there would never be any requirement for level shifting.
Not to say that 74HC series chips should not always work with clean 3.3 V logic - as they indeed should (but Schmitt trigger devices such as the 74HC14 in the non-"T" version just may be fussy). Which is why I continue to suspect some other problems (layout) in your setup.
So no, not safe to conclude that at all. For the meantime however (which is to say, until a board re-design), if it works, well, it works. 