How it's supposed to work:

1. Insert > Media
2. Click on desired photo from among search results.
3. Click "Use this photo".
4. In the Media settings dialog, triple-click to select the file name (plus the "(description page)" link).
5. Command-C to copy the selected text
6. Click in the caption box and paste the contents. (Backspace over the "description page" text.)
7. Be happy that I didn't have to re-type that long name.

What's happening instead:

1. Insert > Media
2. Click on desired photo from among search results
3. Click "Use this photo"
4. In the Media settings dialog, triple-click to select the file name (plus the "(description page)" link).
5. Command-C to copy the selected text
6. Click in the caption box and paste the contents.
7. Get nothing pasted. Be sad.

This problem is reported in Chrome 43 and 44, but it works correctly in (at least) Safari 10.