The word doing all the work in "Sitefinity Dropbox integration" is Synchronization, and almost nobody reads it that way. They see Dropbox bolted onto a CMS and assume the obvious win, which is that storage and delivery move off your server and onto someone else's infrastructure.
Here is the architecture people picture when they switch it on. Dropbox holds the actual image files. Sitefinity holds the metadata. The embed link on the page points straight at the file sitting on Dropbox, so your origin never serves the bytes.
Here is what the feature actually does. Anything you drop into the synced Dropbox folder, Sitefinity consumes and makes its own copy of in the database or filesystem. Anything you upload through Sitefinity, Dropbox gets a copy of going the other way. Both sides hold the full file. You have not offloaded anything. You have duplicated everything, and now you are paying for storage in two places while still serving the bytes from the same server you started with.
The one genuine upside is versioning. Dropbox keeps history on media, so if you roll a file back on the Dropbox side the Sitefinity copy can in theory come back with it. That is a real feature. It is just not the feature the name sells you.
Sync is an honest word for what this is. It is the wrong word for what people actually want, which is real CDN and external provider support, where Sitefinity stores a reference and a third party stores and serves the file. The team almost certainly knows the gap and shipped sync because it was the tractable version to build. Worth knowing before you plan a media strategy around what turns out to be an offsite backup with a CDN's name on it.