That's not correct, you can do both (as I recall Asianese did this last year). The topics covered by both subjects are quite different; the Statistics course focuses more on data analysis/inference and probability, meanwhile Discrete Mathematics delves into stuff like sets, counting and mathematical induction (that's probably a very crude explanation but you get the general idea).
OP, you don't have to do MATH1004 if you don't want to, it isn't a prerequisite for MATH2069 so I believe they would teach you most of the relevant content anyway. If, however, you decide later on to pursue programming and computer science, I would say that MATH1004 is definitely needed.
I'd actually recommend that if you can't decide between MATH1004 and INFO1103 you should do both. MATH1004 is only 3 credit points so you would only be slightly over the standard workload, which shouldn't be too difficult to manage if you are a good student. And if it is, you'll have an idea of what you like more after a week or two of doing both subjects, so you can drop one without a problem if you so desire.