Why does bringing TL072/TL074 non-inverting input low cause output to go high?
Try learn something about allowed Common-mode Input Voltage Range. 
The Common-mode Input Voltage Range tells you the voltages at the inputs that cause them to work properly or to not work.
As for your problem look here 



And here at question "What other features of op amps should the user know about? " 
http://www.analog.com/library/analogDialogue/Anniversary/6.html
http://www.planetanalog.com/document.asp?doc_id=528175