Seems partial truths were amplified out of context, and that is not doing justice to Canonical's Snaps. I would have preferred to have heard the full context and then made up my own mind about snaps.
The crux of it is, that yes Canonical's own Snap Store backend is not open source (same I suppose as Google's Play Store), but they have pointed out you do not have to use that Snap Store, and anyone else can actually host their own Snap Store using the front end open source software. The linked article provides a link (near the end) to a blog post explaining how this can be done.
As far as snapd goes, firstly it is open source, and secondly you can actually run snaps without even using snapd. The packaging format is an existing, documented one used by most distros. The tools used for confinement are existing third-party ones, already used in other distros. For example, Debian and the SUSE family also use AppArmor, as described in the Arch wiki, while its main rival, SELinux, is more complicated and mainly used in Red Hat and its derivatives.
There was an issue also a long time back with snapd using a lot of system resoirces, but I'm not sure if that is an actual issue any more (compared again to Flatpaks and AppImages).
Given all that it does not look like snaps have been given a fair deal. I'm not saying they are better than Flatpaks or AppImages, but I know AppImages have had issues with not having any in-built package update manager.
See Canonical documents how to use Snaps without the Snap Store
Despite what you may have heard, it's not as proprietary as the trolls think