Interesting, licensing is quite complex particularly in the online space (since worldwide licensing providers have different terms and opinions).
Local licensing is very straightforward in the US (and most other countries), which is why there aren't "one station fits all" solutions like Live365 for local stations.
I know the owner of Live365 personally, and I very much doubt that he or any of his staff have 'cut corners'. It doesn't even make any sense, you either pay royalties to licensing bodies or you don't, there's no corners to be cut.
Fact is: If you broadcast from the USA (on a USA IP address), with listeners in the US, Live365 will cover you. Nothing misleading there. As for having listeners in other countries, that's the grey area. Licensing bodies in other countries seem to encroach on licensing requirements (e.g. a listener from the U.K requires a PPL/PRK license, even if you are broadcasting from the US). As for whether that's legally binding or not is another question, it has certainly never been challenged in a court, and is unlikely to be.
Funny thing is that PRS covers you globally (source), downside is, you need to be broadcasting from a UK IP address. As you can tell, it's all very complex for internet streaming. The good thing is that it's slowly adapting and changing. Go back 10 years and it would appear as a war between music licensing bodies worldwide, with emails being sent to you from licensing bodies around the world demanding you pay royalties (source: I ran an internet radio station and have plenty of those emails).
Either way, don't scare new broadcasters. Live365 is a great solution for an all-in-one licensing solution when broadcasting in the USA.