Short answer: yes for public content and personal use. The nuance is worth reading.
Copyright law in most Western jurisdictions recognises a concept called fair use (United States) or fair dealing (UK, Canada, Australia). Under these doctrines, making a personal, non-commercial copy of a work you have lawful access to — for time-shifting, format-shifting, study, criticism, research, or reporting — is generally lawful. Saving a public Facebook video to rewatch offline is functionally identical to recording a TV broadcast with a VCR — the 1984 Sony Betamax decision in the US established that kind of format-shifting as fair use, and the logic has held ever since.
Public versus private content is where most confusion lives. A video posted to a public Page or public profile, visible to any incognito browser without signing in, is indexed by search engines and retrievable by any third-party tool. Saving that video raises no novel legal question. A video posted behind a "friends only" privacy setting or inside a closed group is a different story — but MediaFetcher does not bypass login walls and does not have the technical ability to reach those videos in the first place. If you cannot open a Facebook video in an incognito window, no public downloader can reach it.
Meta's Terms of Service prohibit scraping and automated collection of data. Those terms are a private contract between you and Meta, not criminal law. Breaking them can get your account suspended; it cannot get you arrested. The Electronic Frontier Foundation has long defended fair-use downloading tools, including during the 2020 episode when the RIAA tried to have youtube-dl removed from GitHub and the EFF forced a reversal. The same legal reasoning applies to Facebook downloaders.
Facebook Reels add one wrinkle: Meta licences third-party music for creators to sync into Reels through its own deals with the major labels. When you download a Reel, the licensed audio is baked into the file. That is fine for personal use. Republishing that same Reel to TikTok, YouTube Shorts, or any other platform may trigger Content ID claims on those platforms because their licensing is separate. Journalism and criticism uses — quoting a Reel in a news report, analysing it for a review — sit comfortably under fair use even with the music included. Commercial reposts do not.
What is not legal, anywhere, is redistributing copyrighted Facebook content as if it were your own. Downloading a news outlet's video to watch offline is fine; re-uploading it to your Page for ad revenue is copyright infringement. Downloading a creator's Reel to study the edit is fine; reposting it without credit is not. The rule of thumb is straightforward — personal consumption is safe, commercial republication needs a licence.
This is general information, not legal advice. If your use case involves journalism with commercial distribution, talk to an actual lawyer in your jurisdiction.