I wonder if this is meant to rankle the ambassador. After all, the guy came in, saw a tragedy and asked for thanks. If the thing he wants thanks for was not actually desired – his whole purpose there is thwarted. He does not speak again so it is possible that this serves Horatio’s possible purpose in saying it and that is shutting the ambassador the hell up.
I don’t think Horatio means to implicate Hamlet. I think he just wants the English ambassador to check himself. A major crime scene is not the time for asking for or receiving thanks or reporting executions. Just as a general rule.