First of all, their point doesn't depend on Switzerland being in bad shape or not. They're not saying a country's situation solely depends on this, but that it's a factor. There are lots of other factors at play in Switzerland and most any other country.
Second, there usually is another layer in most of the US (and Canada, for that matter) which doesn't exist in Switzerland: the county. I think that's more likely to cause inefficiencies than federalism alone.
Also, I'm not actually sure Switzerland has more bureaucracy. It mostly seems comparable in my experience having lived in both countries. Are there any metrics on this?