The problem is somewhat deeper: you can construct HTML/CSS combinations, which are
rendered differently by the browsers. Thus you can have e.g. a start
page or a menu which contains different links - depening on the browser
of the user, all but one links are hidden - thus, from the link which has
been clicked you can derive the browser of the user.
Example:
<STYLE > #header {margin-bottom: 3em;}
html>body #header {margin-bottom: 1em;}
body { color: purple; background-color: #d8da3d }
html>body {color: #d8da3d; background-color: purple;}
</STYLE>
<font color = "purple">You are not using Iceweasel</font>
<font color = "#d8da3d">You are using an Iceweasel compatible browser</font>
The only thing to avoid this kind of profiling is to actually USE
the same browser..