Well, we just don't know. However, what always made me curious is how the quote goes on:
‘Something has crept, or has been driven out of dark waters under the mountains. There are older and fouler things than Orcs in the deep places of the world.’ He did not speak aloud his thought that whatever it was that dwelt in the lake, it had seized on Frodo first among all the Company.
This indicates quite strongly that the Watcher was specifically picking the ringbearer. But I somehow don't think that those “old nameless things” would by themselves sense and fancy the ring as much as men, elves, orcs do. Saruman is the only Maia who succumbs to it, but he is IMO a special case (Maia of Aulë like Sauron, and so on). The other examples of ancient beings don't care much about the Ring:
- Bombadil. Completely indifferent, though he knows quite well of the Ring's powers.
- Durin's Bane. Not sure here, perhaps the Balrog was just too busy with Gandalf to focus on Frodo+Ring.
- Treebeard. Well... he never gets near the Ring, but like old Tom he doesn't really seem bothered much by the whole Ring war business at all.
- Smaug. Not sure here either. It is said that dragons devoured some of the Seven, but apparently that destroyed those rings. So much for Precious.
- Perhaps most relevant: Shelob. Paralyses Frodo, but does she in any way go for the ring? No. Sure, Sam attacks before she has much time. But at least Gollum assumes that Shelob would ignore the Ring (and leave it for him to pick later) when eating Frodo. (Gollum may of course be mistaken here.)
I think that, if the Watcher is such an ancient creature, the only reason it would immediately grab Frodo with Ring is on Sauron's account (if not the Balrog's or – unlikely – Saruman's). Perhaps we can't say Sauron controls it, but I believe that he has at least some influence on it.