As you state, FCC approval is related to emissions - and you must comply to sell a product. If you cause interference, you could get a hefty fine unless you can prove your product wasn't being used as intended. CE approval is effectively the same as FCC for Europe, but includes requirements for immunity (conducted, radiated, and ESD). I don't think it includes safety.
UL/TUV/etc testing is safety related, and actually handled by non-government (although regulated by OSHA in the USA). It is not required to sell a product - but will be for you to get insurance, and not having it could have a big impact to your business if there are cases of people getting injured/killed by your product. Safety (& immunity) is obviously a big deal for many modern products like motor vehicles, with complex engine control systems, etc.
I'm happy to be corrected on the above, as I don't normally get involved in safety - most of my designs are under 15W (battery or plug-pack), or they are one-off industrial control systems checked over by an EE where necessary.
I think it is safe (ha ha) to say that these guys won't bother getting UL. This isn't a consumer product, will be sold in pretty small volume, and would not be left alone while in operation. Although they offer international shipping, they've said it will come with US mains connectors - not sure what they're doing about the differences in voltage. I would expect them to be pretty careful with regards to electrical safety though - and in the updates they do talk about relay lifetime, not their not complete amateurs.
Out of interest, has anyone found a toaster oven to actually be useful for reflow? Or even one of those cheap ebay "reflow ovens"? Every time I've done it, I've ended up with plastic parts (connectors) that are burnt, and other parts that haven't properly reflowed. I'm quite happily using an old electric frypan, and get really good results. When a project has components of both sides of a board, that requires me to hand solder (iron or hot air) the parts on the second (usually less populated) side. Again I am very careful with hot-air around plastic parts.