I do not think that they should be allowed to do so except perhaps in certain circumstances such as bots or spam. However for each forum it is the responsibility of each individual forum moderator to keep it clean. Allowing moderators to infract users or enforce site rules outside of their forum seems a little excessive, after all, that is why there are global moderators that have a bit more time/power/responsibility.
Vote and discuss.
InB4 moderators vote to maintain power