Why didn't Sam have a problem giving The Ring back to Frodo?

[Sparrow]

' Here it is!' Slowly he drew the Ring out and passed the chain over his head. 'But you're in the land of Mordor now, sir; and when you get out, you'll see the Fiery Mountain and all. You'll find the Ring very dangerous now, and very hard to bear. If it's too hard a job, I could share it with you, maybe?'

'No, no!' cried Frodo, snatching the Ring and chain from Sam's hands. 'No you won't, you thief!'

I don't know if this scene has been discussed before (it seems like it would make a particularly good topic), but to my mind Sam does not actually relinquish the One Ring of his own will. Frodo snatches it from him, only after Sam offers to 'share' the burden. This could seemingly be construed as a sign that the Ring was having an effect on Sam, but we will never know because Frodo snatched it away before Sam could react.

~Sparrow