You need to quote the asterisk with a comma:
#+begin_example
,* I am not supposed to be a section
#+end_example
See
(info "(Org) Literal Examples")
--
Nick
"There are only two hard problems in computer science: cache
invalidation, naming things, and off-by-one errors." -Martin Fowler
The asterisk inside the example block isn't escaped properly, and
appears as a header, leaving `#+begin_example` and `#+end_example` to
appear as regular text. It occurs in at least both the HTML and LaTeX
output. Here is a minimal example to reproduce the problem:
* first section
