Okay, here's a workaround:
Go to
https://dav.dropdav.com This provides WebDAV access to Dropbox.
Sign up with your regular Dropbox username (username@email.com) and password.
Install www/cadaver from ports.
Cadaver is similar to ftp or whatever, except it works with webdav hosts. So you do 'open dav.dropdav.com' and authenticate using your Dropbox username/password combo. Then you can pull everything using mget or mput, just hit '?' to get a list of commands. This works for now.
If you need to change your DropDav account info, or delete your account from accessing Dropbox, go to
https://dropdav.com/account.php.
There ought to be a way to use www/sitecopy from ports so that you can auto-synchronize like the Dropbox daemon. But when I run 'sitecopy --fetch Dropbox' I get:
sitecopy: Fetching site `Dropbox' (on dav.dropdav.com in /)
sitecopy: Failed to fetch file listing for site `Dropbox':
sitecopy: XML parse error at line 21: not well-formed (invalid token)
Anyway, using cadaver works at least well enough to manually fetch/update the Dropbox contents. Not having auto-sync is something I can deal with. It beats using the web-interface.