The Ring works by desire

[Noxomanus]

In this forum it's often stated the Ring worked by letting the bearer think he could control it's power or by clinging on the greatest power of the wearer.

I personally don't think this is the case,but rather that the Ring worked by what the bearer desired.Sauron himself seems to have worked in this way (offering the Mirdain knowledge,the Dwarves or Erebor wealth and Saruman power,wich all of them desired)As the Ring has part of Saurons spirit,it's only obvious it would work in the same way.Gandalf himself said that the Ring would make terrible use of him as he'd use it to do good.Wanting to do good was what was Gandalfs desire. Galadriel and Elrond would probably be deceived in the same way.On Gollum,it worked by making use of his desire for knowledge and for a beautiful birthday present.Probably also of his paranoia,wich made him desire to be invisible.It nearly corrupted Frodo by making use of the burden it was for him in Mordor.The burden exhausted,and thereby weakened him,making him susceptible for the desire to claim the Ring for his own and use it's great power.It also tried to corrupt Sam,because he,as a gardener,feared for the destruction of plants and the destruction they already experienced and how he probably desired to heal all these hurts.It wasn't for nothing that he imagined himself as a master of gardeners when he wore the Ring.The only other one really resisting the power of the Ring seems to have been Bilbo,as he might not have had a real desire.He did have the desire to silently escape from the Sackville-Bagginses however.But this was a small and innocent desire wich the Ring could not really make use of.
Tom Bombadil is a different story as he was completely happy as he was and didn't have a desire at all,as such the Ring didn't have power over him.
In this way,even the Valar might have been susceptible to the power of the Ring,as they probably had desires as well.