ANSWER:

Well, first off, using Dropbox as a deployment-platform is a bad idea. There are more suited tools to do this, I’m thinking about rsync and/or git…

Nevertheless, you probably installed DropBox with the root-user. Don’t do this, install it as the apache-user. The deamon will run under the apache-user and will create files that apache has rights to read/write.

But, and I can’t stress this enough, you should be on the lookout for better alternatives.

by Bart De Vos from http://serverfault.com/questions/382869