I’m going to make you through an install just to Show the possible problems. I think your tutorial lacks some important hints.

So here I'll try installing it with your easy setup package.

For the server install, I went ahead and created a Debian 7 VPS just for this.

hostname=radio.example.com # This is here, just because...
hostname $hostname
sed -i 's/^127.0.0.1\tlocalhost/127.0.0.1\t'$hostname'\tlocalhost/' /etc/hosts
apt-get update
wget http://apt.sourcefabric.org/misc/airtime-easy-setup.deb
dpkg -i airtime-easy-setup.deb
apt-get -f install

Here you have to setup Icecast2 and configure, choose yes, enter your hostname for Icecast2 server. Specify passwords for Source, Relay and Admin

apt-get update 
apt-get install airtime sudo

Let's check the system:

airtime-check-system

Ok, everything is green, so we know it's working. Airtime is installed as well.
Weird but it didn't ask me for anything, including any passwords. So let's

airtime-easy-setup            # Just to confirm all is installed
dpkg-reconfigure airtime

Choose yes, enter FQDN, install apache2 vhosts file, NOT configure Icecast2 since we already did that
It finished, saying all is OK.

Wait... It still didn't ask me for a password! Ok, no problem… I'll go ahead and create a password manually.

sudo -u postgres psql airtime
update cc_subjs set pass = md5('your_new_password') where login = 'admin';
\q

Now, let’s check our installation by firing up your favourite browser and logging in.

Login, add a few media files. Create a playlist/smartblock, go to calendar, add a show. Add some content to your show. When your show starts on the scheduled time, click on listen button. If you hear the show, all is OK. Nice and easy.

Up till here we didn't do any configuration except the ones during installation. But after a closer inspection, I realized that /etc/icecast2/icecast.xml was reset. The passwords are now shown as "donthackme" instead of the ones I setup.

So I guess even though I modified it with airtime-easy-setup and chose NO during dpkg-reconfigure airtime, they are modified.

Now I have to change them again and update them manually from the "Streams" section in admin interface or I have to run dpkg-reconfigure airtime again and set them from that interface.

On the other hand, looking at the wiki I can summarize it to these commands:

sudo gdebi airtime-easy-setup.deb
sudo airtime-easy-setup
sudo dpkg-reconfigure airtime

Wait, what about all those other steps I had to go through?

airtime-easy-setup DID not install the dependencies. 
Airtime DID NOT setup an admin password. Or didn't let me know if there's a default one.
Icecast2 had it’s passwords RESET.

What I am trying to say is, for people who are not that familiar with these systems your Wiki tutorial is either outdated or confusing.  That's why I am suggesting to go through all the steps yourself and reevaluate the tutorial. Surely you can make it better. ;