I actually did Higher maths though I didn't apply for medicine at uni.
For medicine I would think that you only need statistics to understand drug trials, false-positive rates and that sort of thing and other than that just basic stuff (the kind of maths you see in biology or chemistry). In Higher maths there is very little statistics if any (and I did just check the 2015 Course Specification to double check, which was the most recent I could find) so I think it would be pretty irrelevant.