The first issue is security. Loads of text editors create temporary files (.swp, .php~, etc) in the same directory as the file you're editing. These can render as text instead of going through php, thus revealing things like database secrets and such. Now, this problem won't always occur and can be configured around.
However, perhaps the bigger problem is that this is simply a bad workflow when a better one exists. For "live editing", run a local webserver. Don't expose your playing around to the world, potentially breaking your site for others. Heck, if it's a static site, just run "python -m SimpleHTTPServer" if you like. Second, for deploying, you should have a better process than "sync this directory". Specifically, you should have git hooks that handle deployment if you want don't-think-about-it instant deployment. Preferably you have CI that deploys after it passes a few tests. Using git also has other benefits like letting you have commit messages, easy rollbacks, different branches (which you can auto-deploy to test / dev / etc).
Basically, the problem with using Dropbox or BTSync to edit websites is that you rarely want to throw partial changes to the world, and file sync programs like to sync as often as possible. It's a cool idea, but those sync programs simply don't replace proper version control and CI.
I'd even prefer rsync if you're not using version control simply so you can control when it syncs and setup complex excludes / shell scripts to run around it. You could easily have a script that runs a minimizer and then rsyncs the output while having rsync exclude any potentially accidental files. You can't do that nearly as easily with the workflow the author is talking about.