Why does Claudius suspect Hamlet "puts on his confusion" in Act III of "Hamlet"?

Claudius is confused over Hamlet's behavior but I don't think he has ruled out madness completely. The entire line from which you quote is:

And can you, by no drift of circumstance,

Get from him why he puts on this confusion,

Grating so harshly all his days of quiet

With turbulent and dangerous lunacy?

Claudius is talking with Rosencrantz and Guildenstern, trying to find out the reason for Hamlet's strange actions. Here he mentions lunacy or madness. Earlier, after watching Hamlet with Ophelia, Claudius says

Nor what he spake, though it lack'd form a little,

Was not like madness. There's something in his soul

O'er which his melancholy sits on brood;

So Claudius' intuition tells him that Hamlet is not insane when he is with Ophelia but there is "something in his soul" which is making him unhappy. Whatever the reason, Claudius sees that Hamlet is a threat, especially after watching "The Murder of Gonzago". He has Rosencrantz and Guildenstern watch him carefully and says, "Madness is great ones must not unwatched go." It seems that with his act of madness, Hamlet is also driving Claudius "mad" trying to figure out what Hamlet is up to.