Your comparing apples and oranges.
Also from dictionary.com:
In the context of ordinary argumentation, the rational acceptability of a disputed conclusion
depends on both the truth of the premises and the
soundness of the reasoning from the premises to the conclusion.(the encyclopedia entry concerning Premise)
Inferences and premises are in separate categories. If the phrase "jesus walking on water" is not part of an argument then one is free to determine whether or not it is or is not a logical inference. But the instant that phrase is placed in an argument it is no longer an inference but a premise and thus is either true or false, not logical or illogical. the only way the phrase could be considered an inference and stil be part of an argument would be if the phrase were the conclusion of an argument for indeed an argument's conclusion is also known as an inference. and then one could determine if it is logical or illogical in whether or not it follows from the premises of the argument. However in this instance the phrase itself is no longer a premise but a conclusion. Even if "jesus walking on water" were a false statement it can still be placed in a logical argument:
P1: Jesus was a holy man
P2: All holy men walk on water
----
Therefore,
Jesus walked on water
This is a logical argument because if the premises are true then the conclusion necessarily follows. However it is not a sound argument because P1 is debatable and P2 is false as we know of no holy men in this day and age who walk on water. Now to make the phrase a premise
P1: Only holy men walk on water
P2: Jesus walked on water
----
Therefore,
Jesus is a holy man
Again this is a logical argument but it is not sound because P1: is false, not only do we not know of any holy men these days who walk on water but we do know of different insect species as well as at least one species of lizard who are capable of walking(or running) on water. Also P2 is at most debatable because it can neither be proven true or false.
Do you see the difference? At most an inference can be the conclusion to an argument but the instant a phrase becomes a premise it is no longer by definition an inference and thus trying to say it is or is not a logical inference is pointless because a faulty premise can still be used in a logical argument. The argument just won't be sound.