More information:
The section in the all.css generated CSS file only specifies h1 through h3, hence why heading 2 and heading 3 dont get affected as they're really H4 and H5.
The lines in question in the css are:
h1,h2,h3,h4,h5,h6{font-family:'Roboto',sans-serif;font-weight:400;color:#023482}
h1{letter-spacing:0px;font-style:normal;font-weight:300;font-size:24px;line-height:28px;margin-top:0px;margin-bottom:21px;text-transform:none}
h2{letter-spacing:0px;font-style:normal;font-weight:700;font-size:18px;line-height:21px;margin-top:0px;margin-bottom:21px}
h3{font-style:normal;font-weight:700;font-size:16px;line-height:21px;margin-bottom:21px}
I can't work out where these are coming from. And this is in a pretty much brand new install of moodle and elegance. It also affects the section names as they are h3 as well.
Edit: Here is a guest accessible site so you can see for yourself there is no class affecting it: http://web3.mtaustin-h.schools.nsw.edu.au/course/view.php?id=5