Well, that kind of rules out a 3rd Party App causing the issue. Since this just sort of "popped-up" on this forum and the Moto Forum, makes me wonder if the problem is with the Chrome update? I have not updated the Chrome app on my phone, or my wife's phone (just haven't had a reason to...been too busy). Both of our phones are on Chrome version 28.0.1500.64. I have tried several times to re-produce the issue on our phones and can't. Swype works great in the Text app and in Chrome. Curious to know what version of Chrome you have?
Hold off on the hammer just yet.
September 5th 2013 is the newest update version 29.0.1547.72 this is what is on my phone. The issue started me around August 26 2013. I recall this cause it was the day I flew home and had hell of time registering for the go go in flight internet..