Is there a cheap touring bike that is as light as a road bike
There was a trend of these bikes about 8 years ago. They weren't called touring bikes, but Century or Relaxed Geometry. This is a typical example:

Trek Pilot - http://www.trekbikes.com/us/en/bikes/2006/archive/trek/pilot21/#/us/en/archive-model/details?url=us/en/bikes/2006/archive/trek/pilot21

However, they seemed to all disappear from the big manufacturers a couple years ago.
Plenty of small brands still in this market. I'd look into Salsa for examples. 

If you've got the cash to spend, this is the bike I would recommend. Volagi Luscio.

http://www.volagi.com/wp-content/uploads/2014/02/Cyclist-Magazine-2014-Liscio-Review.pdf

I've test ridden one and they are exactly what you are looking for. I think any bike
in this niche today is likely to have disk brakes, rather than the long reach brakes
on the Pilot. So I'd start looking at various road bikes with disk brakes and see if
you can find the geometry you are looking for. 

If you can find an old Trek Pilot or Specialized Sequoia, those would be relatively good
frames to start from. With the right components, you could easily get around 10 kgs bike
weight. 

You wouldn't want to carry 90lbs of touring gear on these bikes, but a moderate load would be just fine.