Troll sat alone on his seat of stone...

You fellow Tolkien-lovers certainly remember that part of the Fellowship of the Ring, where the hobbits and Strider find the three stone trolls long before encountered by Bilbo. Sam then sings a rhyme of his own making:

Troll sat alone on his seat of stone,
And munched and mumbled a bare old bone;
For many a year he had gnawed it near,
For meat was hard to come by.
Done by! Gum by!
In a cave in the hills he dwelt alone,
And meat was hard to come by.

Up came Tom with his big boots on.
Said he to Troll: 'Pray, what is yon?
For it looks like the shin o' my nuncle Tim.
As should be a-lyin' in the graveyard.
Caveyard! Paveyard!
This many a year has Tim been gone,
And I thought he were lyin' in the graveyard.'

...

The full text can be found here. It was also put to music by the wonderful Tolkien Ensemble [link] – I recommend!

I love this passage, which is a welcome relief during the otherwise gloomy flight to the ford. But I wonder about this song. Recently I read that the hero of the song is actually Tom Bombadil, which never before occured to me (perhaps because in the Czech translation the name in the song is changed to "Tomáš" for metric and rhyming reasons). I had always seen this Tom as simply a generic fictional adventurous lad, in a similar way as the "merry old inn" in another hobbit song is not the Prancing Pony, nor any other real inn, but just an invention by Bilbo, who made that song. I tried to make some research about the connection of this song with Tom Bombadil and I'm still not sure about it.

I see some reasons for it:

• The song was apparently put together by Sam and first sung several days after the hobbits' visit to the house of Tom Bombadil (who is sometimes reffered to as simply "Tom"). So it is conceivable it was made under this impression
• It was included in the collection of poems The Adventures of Tom Bombadil, which strongly suggests the connection (though in the same collection there are also many other hobbit songs and poems which have nothing to do with Bombadil).
• The carelessnes of Tom's challenging the troll, as well as the emphasis on his big boots – these things fit well with the description of Bombadil.

But there are also several arguments against:

• Obviously Tom Bombadil who was referred to as the eldest and was a wholly mysterious being most probably didn't have any uncle named Tim, lying in a graveyard (with or without his shinbone). On the other hand, this song is obviously an invention by Sam Gamgee, so even if it is about Tom Bombadil, we cannot expect it to be accurate description of any (in Tolkien's world) real events or connections.
• The Tom of the song does escape the troll, but his adventure is eventually a failure: He does not recover his uncle's bone and "his bootless foot is lasting lame". This doesn't look like Tom Bombadil: He bosses the Old Man Willow, he effortlessly vanquished the Barrow-wight – and now he isn't able to outwit an ordinary old troll?
  
• There is a different (perhaps older?) version of the song, which reads: "Up came John with his big boots on. (...) it looks like the shin o' my nuncle Jim". There is even a recording of JRRT himself singing this version of the song: [link]. Whatever the reason for the change in the published version was, at this stage it certainly wasn't intended to be about Tom Bombadil.
  
• After all, Tom is a common hobbit name, a shortened form of Tolman (such as Sam's future father-in-law and brother-in-law).

What do you think about it? Maybe there is a definitive answer somewhere in the History of Middle-earth or the Letters. Or is it open to speculation? I would like to now.

Edit: The reason why I was interested in this song in the first place was because I had an illustration in mind. Eventually it doesn't feature Tom but only the troll, nevertheless, you can look at it here.