Try the magic word 'Intranet'
Still, I'll admit the most of the time it's the Internet you want to access rather than an Intranet.
In any case, other objections should be obvious :
1) Lynx is not large and a system is not about to stop working by not shipping a media player..
2) The software respository might be blocked in the firewall
3) It requires a download. This is not necessarily free, or reliable, or fast.
4) In the event of a failure to root prompt, if I remember correctly there is no help to speak of. Using apt-get requires remembering to use apt-get, whilst at least an installation of lynx means the documentation can be studied.
5) It's one more thing that can break. Installation of programs requires a working installation infrastructure. If it's there by default, this is less important.
6) apt-get requires an accessible repository. I cannot remember if there are fallback repositories, but it does not help if you have a dead box and no record of alternate repositories.
In short, the argument would be much better applied to superfluous functionality such as games, music players etc