Nursery Rhymes: Three Blind Mice

I decided, as I had so much fun with the last posting on nursery rhymes, that I would do another.
Tonight I picked another well known one that is believed to have a story related to the Mary, Mary, Quite Contrary nursery rhyme.

Just the nursery rhyme itself is a tad bit unsettling, I think. Though, honestly, it also amuses me so very much.
It goes:

Three blind mice, three blind mice,
See how they run, see how they run,
They all ran after the farmer's wife,
Who cut off their tails with a carving knife,
Did you ever see such a thing in your life,
As three blind mice?

What do they claim this is about:
This one is said to be talking about Mary I Of England (Bloody Mary), again.

They claim that referring to her as a farmer's wife has to do with the large estates that she and her husband owned.

And that the three blind mice are to be the three Protestants bishops who were plotting against the queen, who were burnt at the stake.

Now, something I did not do with the last nursery rhyme:

Why this doesn't make sense:
Well, what does dismembering a mouse have to do with a man burnt at the stake? I can get that you would call them blind mice, if you saw them as so believing in a faith that they are blind to other trains of thought. However, that is such a stretch to connect cutting tails off with burning flesh.
(That last sentence seems, briefly before I disregarded it, as a very unlikely sentence to find in a parenting blog. I am amused. Welcome to my place, sit down and we'll have some tea and biscuit, okay? Okay.)

Also, while the original version of this nursery rhyme is found to have been published in 1609, 54 years after the Oxford Martyrs, the version we know today was not entered into children's literature until 1842, nearly three centuries later... Which might not mean a damned thing, really. Though it also begs the question to why children were interested in something that happened hundreds of years before. 

I always, though, look at these 'behind the story/rhyme' as for pure entertainment and not to be historical accurate. Maybe there are a few rhymes with some real interesting, and true, stories behind them. Do you know one?
[And, yes, of course I have heard about the story behind Ring Around The Rosie, and sadly it is an urban legend.]