What that 2ms time is needs defining. That's from "a brightness level" to "half that brigtness level." Many are confused about this and need more explaining what this time is and what it means.
You should see ghosting on such a display if the image was bright and went to near black.
There is another factor in this time and that is the TEMPERATURE of the LCD PANEL. One complainer had their LCD in a cold basement. The ghosting was terrible but as a test I had them turn on the display an hour before they wanted to use it. The ghosting was still there but within reason. Not nearly as bad as it was when it was stone cold.
This does not fix your issue but is to arm you with more about what this is. If you want ghost free displays you might have to go back to CRTs or try a PLASMA display.
Bob
I am having an unusual problem with my monitor (LG L207WT). Although the response time is only 2ms, i am having ghosting issues while playing video games.In some games more intense than in others...but still...i have it. I have noticed that the ghosting is more intense when the displayed environment is darker and on the other hand, i have no ghosting issues at all when the displayed environment is very bright. I dont know if you agree with me or not, but i dont find ghosting to be normal in a 2ms screen. I mean, i ve heard that there is no ghosting visible to screens with even larger response times, like 5ms. Can anyone please help me on this?
I dont know what other hardware information should i give to help someone understand the problem, since i think its a monitor issue alone. The only directly assosiated hardware is my GPU. Its GeForce 8600GT (yea i know its old, hehe
) with the latest drivers installed of course.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic