Thank you both for your comments. I apologise for not making it clear that I was referring to gui file manager operations.
Last Wednesday night I went to visit a friend and, while he did some further internet searches, I set out to do some tests with various linux iso images on a usb stick. First I booted up lubuntu 12.04 and copied a small file to different local linux and Windows locations. The modified date was preserved. Then I connected to my friend's network and attempted to copy to one of his ntfs drives. As expected, PCManFM was unable to properly discover the Windows shares so I installed Nautilus which made the connection and copied the file. The modified date was preserved! I copied the file back to linux. The modified date was preserved! So I decided to try another distribution. I booted up lubuntu 13.10 and the first surprise was that PCManFM was able to discover the Windows shares. Again when I copied the file to various locations, the modified date was preserved! Meanwhile my friend found this -
http://www.pclinuxos.com/forum/index.php?topic=101923.0
I haven't yet had the time to do any more experiments but I have some ideas about what is happening.
1. The netbook (ubuntu 11.04) connects to Windows shares by auto mounting because it uses Nautilus and that works well.
2. Because the nettop (lubuntu 13.10) uses PCManFM and that doesn't auto mount the Windows shares, I resorted to defining mount points and fstab entries and that's where the changed "modified date" is coming from. I found forum posts that seemed to suggest that ubuntu 12.04 and newer had a problem with auto mounting. Perhaps the authors were misinterpreting the evidence.
3. When I connect to Windows shares using XP, it maintains a record of the shares even when they are no longer valid. It appears that Nautilus somehow negotiates a connection to that list and, once that connection has been made, PCManFM can also use it. I think the connection will survive a linux reboot but not a Windows reboot.
It seems that there is a linux setting which ensures that the file managers will preserve the modified date but it's somewhere in the mounting details. It may take a while but I plan to find and apply the solution. I also plan to post the details here but, since I probably won't understand most of them, it would be helpful if a linux expert could provide an explanation.