Google-analytics – Google Analytics — Question on how it affects search results on Google

Ultimately, there is no way to hide it. Worst case, the competitor can just look at the address of the analytics image loaded on the page.

But what's stopping them from creating a separate email address, registering a separate google analytics account and then just adding their original email as full-access co-administrator?

Short answer: yes.
Long answer: it depends on which version of the tracking code you are using. Meaning that if you are using an older version (urchin.js), you need to copy/paste a different tracking code into your secure pages. (Here is the man page: http://www.google.com/support/analytics/bin/answer.py?answer=55483)