Where the files come from, and why that is the whole product
Most download sites work by fetching the file onto their own server and then handing it to you. It is the obvious design and it is expensive: every byte you download is a byte they paid to receive and a byte they paid to send.
This site does not do that, and the reason is a header.
The measurement
Snapchat serves profile media from two hosts. Asked for a file from a foreign origin,
both answer with access-control-allow-origin: * — the header that tells a browser
it may read the response. A media address resolved from a server in Moldova was then
downloaded intact from a home connection in Vietnam, which proves the address is not
tied to whoever resolved it.
Together those two facts mean your browser can be handed the address and fetch the bytes itself. So it is.
The exception, stated plainly
There is one place this breaks. The profile picture and cover image sit on a different Snapchat path, and that path sends no cross-origin header at all. A browser will display those images but will not let a script read them, so they cannot be saved under a real filename without help.
Those two files, and only those two, are relayed through this server. They are between 2 KB and 200 KB.
It would be easy to describe the site as "nothing ever touches our servers" and quietly relay two files. The reason not to is that anyone can check, in about fifteen seconds, with their browser's network tab open.
Why it matters to you
Three things follow from the bytes not passing through here.
There is no queue and no speed cap. A site paying for your download has every reason to throttle it. This one has no bandwidth cost to control, so your download runs at whatever Snapchat and your connection manage between them.
There is no copy to store. A server that never receives a file cannot keep one, cannot leak one, and has nothing to hand over.
It cannot silently become false. The behaviour is visible in your own browser. If this site ever started routing media through itself, the network tab would say so before we did.