factor, you are correct in stating that probate may not be needed, however some form of official agreement that the estate doesn't owe money to the government, and that it can be distributed, always has to be obtained.
I an always a bit wary of saying "probate is not (or may not be needed) as the enquirer might interpret this as being able to go ahead and distribute the estate without doing the admin that is needed.
.....not in this case of course as you posted the link but I do think that its needlessly confusing to call the process "probate" if the estate exceeds a certain amount and something else if the amount is lower.