How to Recover Data when OSX cannot? There is only one .tex file which I would like to restore in my system. 
My system is El-Capitan 10.11.5 in Macbook Air 2013-mid. 
Problems


I have Time Machine backup but it is 3 days old and does not have the latest .tex file that I need. 
There is no sufficient tools in the Internet recovery mode started by ALT-CMD-R. I cannot mount my normal Mac HD partion. There is FFFF:FFFF:FFFF:... in the type. I can detect its size correctly however. I cannot reach the HD. I cannot even duplicate it to external HD i.e. in the internet recovery mode. 
When I start to reinstall the system in Internet recovery, I see no discs in the stage Select the disk where you want to install OS X. So something badly wrong with partitions. 
I cannot bypass refind because I cannot choose the startup disk. I contacted the developer but he has not provided yet the exact directories/files which to remove for the uninstallation. 


Final move in Linux Live USB


Copy data. Open it in another OS X installation. 
Install Debian Linux on the whole SSD disc. 
Install OS X on the Internet Recovery. 


Find OS X disc by lsblk and do 

http://unix.stackexchange.com/a/11264/16920
sudo dd if=/dev/sda of=/media/ubuntu/ntfsDisc/sda.hfs.dmg bs=512 status=progress


so it took 64 minutes about for 70 Gb. You do not need status=progress. You can ask the status also by pkill -USR1 -x dd. 

I did now full install of Debian for the whole SSD disc. Started internet recovery mode and installed OS X in very small partion of the disc because you cannot resize it easily afterwards. Trying to do any disk partition operations on OS X side etc Disk utility was horrible. Trying to resize also the OSX partition with Ubuntu installation media was horrible, never finished. 



How can you recover data when OSX cannot?
You can't recover data directly - in the sense of recovering data lost by accidentally deleting files or formatting a volume - in Internet Recovery Mode/Recovery Mode because no appropriate tools are available in the Base OS X system.

You may clone a disk or volume with dd to an external drive and check the data on a second Mac using a recovery app like Data Rescue/Disk Warrior or Lazesoft Mac Data though. IIRC some of the apps even allow you to create a recovery DVD/thumb drive and by booting from this modified recovery OS X you may check your Mac's disk directly.