The song is quite old, but those interpretations of it are quite modern and seem to have no foundation at all. A form of Three Blind Mice appeared in Thomas Ravenscroft's Deuteromelia of 1609, but it wasn't any longer then than it is today:

Three blinde mice

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For the sake of completeness, here is the Ravenscroft text.
-Joe Offer-

Three Blinde Mice,
three Blinde Mice,
Dame Iulian,
Dame Iulian,
The Miller and his merry olde Wife,
shee scrapte her tripe licke thou the knife.