There's something to that claim. Sending uncompressed (i.e. not transcoded) video content over the internet can easily saturate your internet link.
Do you have CIFS/Samba, in other words Windows Network Explorer access to the files on the NAS via your local network? If so try directly opening a video and look at the network dashboard of the NAS and/or your computers task manager (performance -> ethernet tab) to see to what mbit bandwidth the not transcoded stream amounts too.
Consider that the exact same mbit bandwidth will be needed using Synology QuickConnect to view media from outside of your local network.
If you want to work around all that you would probably have to look into something that buffers/transcodes your media, something like Jellyfin/Plex or the likes. For that you'd have to look into running Docker on the NAS but that'll plunge you into self-hosting very deep very fast and may be beyond your initial comfort zone.