You could probably find a third party app to get around this, but I discovered that Apple actually does provide an obscure way to get at this text. GUI scripters might be familiar with Apple's UI Element Inspector, which is a free app you can download here [299KB].
This inspector will give you the nitty gritty details of whatever UI element your cursor is hovering over. Think of it as the ultimate "Get Info," or "Get More Info than I ever wanted to know" application. Once you've downloaded the app, you'll need to launch it and then open the Get Info window for the file you're interested in. Hover your mouse pointer over the relevant text in the Get Info window, and hit Command-F10 on your keyboard. This "locks" the information you found at that position in the UI Element Inspector's main window. Somewhere in all that jargon, you should be able to locate the information you wanted in plain text, and -- conveniently enough -- it can be selected, copied, and pasted wherever you like. To make things even easier, read on for a simple AppleScript to do the work for you...
Here's the AppleScript code:
set AppleScript's text item delimiters to ""
tell application "System Events"
set theInfo to the value of static texts of scroll area of ¬
window of process "Finder" as list
set theCount to the number of items of (item 1 of item 1 of theInfo)
set theTexts to {}
repeat with w from theCount to 1 by -1
set the end of theTexts to value of static text w ¬
of scroll area of window of process "Finder" as text
end repeat
set AppleScript's text item delimiters to return
set the clipboard to theTexts as string
end tell
[robg adds: I haven't tested the script...]

