Auto-successes are certainly rare, but that's normally down to the conditions of success, rather than a blanket '1s always fail' rule.
I'm not sure of the current (Second Season) rules for Blood Bowl, but in the CRP it was stated that 1s aways fail (and 6s always succeed) specifically for all Agility rolls. That covers most d6 rolls, but not all. For instance, it would be possible to auto-pass a Go For It roll, if one had a modifier (unless the modifying rule specifies otherwise of course).
The 6s succeed thing certainly isn't a GW universal, since some games (I forget exactly which) have had rules for a 7+ to hit. For instance, you need to roll a 6 followed by 4+.
If '6s succeed' isn't universal, I don't see any reason to think that '1s fail' applies except where stated. (I grant that it is often stated, but the question here is whether it's implicit even when not stated.)