In 2015.10, when you pick "copyright only" or "copyright and contact info" the capture date is not exported.
I cannot say if this is new behavior as I almost always select "all metadata", but I would expect this current behavior given the descriptive titles.
Since the capture date is not exported, it seem reasonable that the import process puts the file creation date as the capture date of the new file.
Give "all except camera and camera raw" a try and see if that includes too much info for your needs.
This makes total sense to me. Unfortunately exporting with "all except camera raw" won't work for me because that will include the caption and other IPTC data that I don't want out on the web. I'd prefer things to work as they had worked at one point in time: that exporting images with "copyright only" or "copyright & contact info" would preserve the original capture time metadata in the resulting file.
I don't know when this changed, but it's something I noticed recently- say within the last few months.
I think the capture date is left out of "Copyright only" and "Copyright & contact info" because those choices leave out all EXIF metadata (camera exposure data), and the capture date/time is part of EXIF.
One option is to use Metadata Wrangler, a Lightroom export plug-in by Jeffrey Friedl. You can include or exclude individual metadata items, and you can save settings as presets. For example, you could create a preset that excludes everything except the capture date and specific copyright/contact information you want to keep.
I just opened LR 5.7.1 to test.
When exporting an image with Copyright only select in the export window the date that shows is the Metadata date which is the date/time of the export. No other dates and not even any fields for a date is shown.
So it is not just LR 2015.10/6.10 that this happens with and IMHO it is as it should be.
If you want to the exported JPG to be right next to the original then select Add to Stack: in the export dialog window. That will place the exported image right next to the original.
Thanks for the confirmation and suggestion. Unfortunately stacking won't work for me, either, as my derivative files (e.g. exported JPGs) live in a different folder than my original/master images in my archives and this isn't something I can change to take advantage of stacking.