Credit to Wes P. of the Dropbox forums for coming up with this idea.
Given the circumstances, it is theoretically possible to sync Dropbox’s installation files through Dropbox itself to sync the same version of the app to multiple devices. This would theoretically allow you to update the app on one computer, and have the install files sync to other versions of Dropbox.
Please note that this is theoretical, and has not been tested on any computers. Do this at your own risk.
It appears that R.M. (aka the Dropbox Wizard, Dropbox Fairy, or Saint R.M.) has left Dropbox. According to several moderators on the forums (one of which mentioned that R.M. had told him what was happening), R.M. had previously gotten a summer internship at Dropbox. Before this, he was just a moderator on the forums, and he recently had gotten this internship at Dropbox. R.M. had only actually worked there for a short time, but throughout this summer, he’d been on the forums on a daily basis, and had answered so many questions and fixed so many problems, he became one of the most popular employees on the forums, despite being only temporary.