Hardware control is done through the internet because it needs to be controlled remotely. The LHC is enormous so you can easily be 10 Km from your the hardware. Not to mention the hardware is also sometimes controlled remotely by researchers at other facilities such as Fermilab. Also we should remember that CERN has pretty much everything hooked up to the internet because they invented it. Which makes the whole situation pretty ironic.

The web, at least: http://ben.web.cern.ch/ben/TCPHIST.html

why is hardware control attached to machines networked to the internet?

Well they might not be able to properly configure a few computers, but let's just hope they got the whole simulating the creation of an entire universe thing down.

Because it's control and monitoring, and the internet is the easiest way of sending around small chunks of data that you recorded to colleagues around the world.

why isn't data recording a one way process?

A brief explanation can be found here http://pv0.info/2k/v.

Ahem, "crackers", not hackers.

Collider Exacts Revenge With Large Hadron Beam

It seems that network security is not near the top of many people agendas over there (it might be now) - even though not having it done properly leaves them open to attacks which could stop them achieving their primary goal.

Sounds like a scene out of "Digital Fortress" by Dan Brown.