Its absolutely incorrect. I've written a synchronous event-based programming system for a project where every single program was absolutely guaranteed to termin

Its absolutely incorrect. I've written a synchronous event-based programming system for a project where every single program was absolutely guaranteed to terminate. Yes, it wasn't fully general, since it didn't support unbounded loops, but it could run many types of programs and they always terminated. When you can make assumptions about a program and its inputs, the halting problem doesn't apply. I mean, just simple observation shows that if you can't make whether your program terminates a condition inside your program, then the halting problem ambiguity as stated can't apply -- you may still not be able to determine if it halts or not, but with enough constraints or assumptions that can be taken as true, you absolutely can know if your program halts or not without executing it.