harry potter - Could Hermione really free the Hogwarts house-elves with her knitted hats?

Could Hermione really free the Hogwarts house-elves with the little knitted hats she hides around Gryffindor Tower?

‘Why d’you wear that thing, Dobby?’ [Harry] asked curiously.

‘This, sir?’ said Dobby, plucking at the pillowcase. ‘’Tis a mark of the house-elf’s enslavement, sir. Dobby can only be freed if his masters present him with clothes, sir. The family is careful not to pass Dobby even a sock, sir, for then he would be free to leave
their house for ever.’

_{Chamber of Secrets - page 133 - Bloomsbury - chapter 10, The Rogue Bludger}

AND:

‘You’re leaving out hats for the house-elves?’ said Ron slowly.‘And you’re covering them up with rubbish first?’

‘Yes,’ said Hermione defiantly, swinging her bag on to her back.

‘That’s not on,’ said Ron angrily. ‘You’re trying to trick them into picking up the hats. You’re setting them free when they might not want to be free.’

_{Order of the Phoenix - page 230 - Bloomsbury - chapter 13, Detention with Dolores}

If a house-elf can only be freed by his or her master or mistress, as Dobby says, how could Hermione free a Hogwarts house-elf if an elf happened to pick up one of her knitted hats, as Ron insists?

This, I believe, brings us back to the question: Who owns the Hogwarts house-elves?

_{Who knew that house-elves could be so complicated?}