This is all about Airport Junction
AIUI▸ - they are providing a much more complex flyover arrangement, so that trains to/from the airport can use both fast and slow lines without any flat crossovers. At the moment I believe the junctions are optimised for HEx to/from the mains, Heathrow Connect was an afterthought.
When they refer to heading south into a tunnel, it is trains heading to the airport - the article suggests Crossrail is a new route, but that's not really correct...
PS - reference to a planning application is basically rubbish as well, Crossrail has an Act allowing it. The local authority will have a final say over minor details only, such as surface finishes.
PPS - Here's a link to a drawing I posted earlier in the main Crossrail thread that shows the new setup at airport junction:
http://www.rail-reg.gov.uk/upload/pdf/s18-xrail-appx2_single_line_GW.pdf Paul