If they are distributing new firmware to their printers, I’m not sure why they would only make it available for 5 minutes.
What would be much more likely is that they require a PSK to download the file. A PSK would be shared over SSL and encrypted - but if the software is open source - it may contain the PSK… but they could always strip it.
Realistically - I don’t think there’s any obfuscation or anything funny going on - just that they aren’t publishing the URL to the package so you have to find it yourself.