I've heard that the verb to welsh has nothing to do with the reputation of Welshmen, but derives from a former Prince of Wales who, being no gentleman, defaulted on his gambling debts.

Having said that, a slightly longer version of Taffy ran:

Taffy was a Welshman,
Taffy was a thief.
Taffy came to my house
And stole a lump of beef.
I went to Taffy's house,
Taffy wasn't in-
Taffy came to my house
And stole a rolling-pin.
I went to Taffy's house,
Taffy was in bed,
So I picked up the rolling pin
And bashed him on the head.

Welsh, from AS wealh, the same word for Briton (Celt) and slave. Which suggests something about how the Saxons made their living.