Correct, that it is an argument that Hamlet has learnt and not one that he has invented. Aren't they all? But the point I put accross was not about the origin of the argument that he uses, but to stress the fact that it is employed only after the killing of Polonius. Where, before this point in the play, is such an argument used? Hamlet always has it at his disposal, yet he would not use it before. He could kill Claudius given a chance and having the physical ability to do so (that, you argue, the ghost does not have) yet he would not before. After this point, he would.
What point do you think I was talking about? Not the point where he rationalises his action, no. But the "sticking of the sword into Polonius" is itself the point, the turn of event where Hamlet has for the first time blood on his hand for the cause of revenge. The killing of Polonius is arguably the only action up until then that Hamlet has not comtemplated carefully, which resembles the decisiveness of his father that he does not normally have. It is a rash action, he misreads the plot (thinking Claudius was behind the curtain and not Polonius). Before that every plot they set up to try and spy on him has been read by him correctly: hiding in the closet, sending Rosencrantz and Guildenstern. It also seems a rash action since he, though suspicious that Claudius is behind the curtain, initially does not really care whom it is that he had killed.
"Nay, I know not, is it the King?"
Later, he repents yet reasons: It seems that the act of hiding and intruding is enough to be killed:
"You wretched, rash, intruding fool, farewell,
I took thee for thy better: take thy fortune,
Thou find'st to be too busy, is some danger."
If one makes it his business to intrude, it is up to fortune what happens to him, since what he intrudes upon may be very dangerous without his knowledge. Hamlet's reasons indeed apply perfectly for Polonius. But though it is his fortune that Polonius dies, it is still a punishable offence that Hamlet has comitted by killing him. The same would apply had Claudius been killed, thus answering the following:
It is a non-factor, for Hamlet would be doom'd anyway even if it were Claudius behind the curtain. Claudius' sin is not for Hamlet nor for the ghost to punish. Personal revenge is not an act tolerated by heaven, not in Hamlet's mind anyway.
After the killing of Polonius and only a moment, though of great consequences, of rash behaviour, Hamlet regains his reasons. But it is changed:
"I must be cruel, only to be kind". Indeed, immediately after this event, Hamlet reveals that he has discovered another plot (the letters) and himself is going to react to it very differently from before:
"But I will delve one yard below their mines,
and blow them at the moon."
This time, those that wrong him will receive more than his criticism and contemplation of their sins. A revengeful soul is not a clean one. Thus to be a successful one, it is important to get one's hands dirty first. No, I don't think that it is a weak argument. The ghost's hands are already dirty, it does not hide it:
"Until the foul crimes done in my days of nature
Are burnt and purg'd away."
Its cause may be just in its own mine; but that's it. And it is fully aware that Hamlet will also burn like itself for the tasks it asks of him. There's no reason for it to interfere with Polonius' death.