How can I securely receive picture/video/file files from anyone via web upload?

How can I securely receive picture/video/file files from anyone via web
upload?

We have a marching band program. Our parents take lots of pictures and
videos. We'd like to collect these pictures and videos. Right now, we ask
them to email us the pictures and videos, but our parents struggle with
file attachments, email attachment sizes, etc.
We're looking for a dedicated external hosted service where anyone can
upload a file that will be stored online in a common area. It would be
ideal if it required no registration, to reduce the friction for a user to
upload files. No uploader needs to see what files were uploaded
previously. An admin can then log in and review the files in the common
area and download them and delete the files.
Sites like Rapidshare and Depositfiles and the like are for anonymous
download, not anonymous upload, so they won't work.
Sites like Flickr and SmugMug allow upload and sharing, which again, we
don't want.
anonfiles.com, anony.ws, and Hide My Ass File Upload all allow anonymous
uploads, but each upload is kept separate, and they're targeted towards
people that want to put a file out on internet that can't be traced back
to them. That's not a requirement for us.
This answer does address the question: Is it possible to allow an
anonymous person to upload to my Dropbox folder?, but it's somewhat
convoluted.