that's how it works. point a free-to-air dish at the right place in the sky, demodulate the DVB-S2 signal, and it's often IP traffic moving through mpeg transport streams.
File system is the wrong word.
What they should have used is file format.
It is not wrong that you can have a file (bits and bytes encoded in the shape described by a file format) on some remote point. If you have an index of those files where you can programmatically choose between multiple files that could even pass as a crude "file system". But I doubt this is what they meant to refer to.
It is likelier they wrongly assumed a file system is the system in which a file is organized, where in fact they meant file format.
I think they were going for a reasonable analogy, especially when a stream is saved to disk to have its contents extracted: each channel contained in the stream can then be thought of as a separate file, not unlike files in a zipped directory.
That's probably better, but also that's not much different on a conceptual level from a "filesystem". Both contain multiple files, and describe where in the overall image those files are. The difference is exactly in the interleaving - a multiplexed media container is somewhat constrained to a packet-based scenario, where individual packets of the constituent files are separated so that video, audio, and ancillary data all reach the decoder at roughly the same time. A pure filesystem is not constrained as such and can put the files anywhere within the container.
A filesystem stored in a monolithic file is not so constrained. I work with Harmonix games as a modder, and they use a bespoke format called "ARK", which is a two-part format. There exists one or more "ARK parts", which in implementation are virtually concatenated, and then the HDR lists a binary offset from the beginning of the first ARK part to tell the games where the individual files are. This could also be called a "container" conceptually. But none of such files are interleaved in any way except for the audio files, which use encrypted multichannel Ogg Vorbis streams plus a bespoke header to aid in seeking.
Plus, the context was explaining it to laypeople, where the specific jargon is less important than imparting knowledge and understanding.
The difference between a file system and a container format is mostly a matter of perspective - indeed OSX literally uses "disk images" as their container format. Is .zip a filesystem? You probably wouldn't want to use it natively on a disk, but for a lot of purposes it's the same kind of thing.