It is one of those words that seems to have been picked up from TV pundits. “Unarguably” has never been common usage in my experience. The supposition of “arguably” is that it an absolute determination cannot be made, but that a strong case can be made for one argument or another. When commentator on TV says it, they mean, ” a case can be made, but I am not necessarily making it.” Your daughter was complimenting Rick’s chicken, but was open to the possibility that Bob’s chicken down the road was just a bit better.