So the show never included the context that he was human?
This is the full original song, and from old recordings of the show, I think they only every had the first verse. Though I'd still not assume he's a dog just from the first verse (either human or a "bear" in the show's context)-
Mama, don't whoop little Buford
Mama, don't pound on his head
Mama, Don't whoop little Buford
I think you should shoot him instead
Buford brought home his report card
Buford was proud as could be
At last he had passed through the 3rd grade
And Buford is just 23
Mama, don't whoop little Buford
Mama, you'll just be a wreck
For Buford is studying Judo
And he'll break your scrawny ole' neck
When Buford was five, he was smokin'
And drinking hard liquor at six
At seven, he learned about women
At eight, Buford got his first fix
Mama, don't whoop little Buford
You'll never know how Buford feels
Buford is good to you, mama
He brings you whatever he steals
Now Buford is gone, what a pity
At last we found happiness
We bought a new home in the city
And we won't give him our address
So, Mama don't whoop little Buford
Mama, don't knock out his breath
Just teach him to be a folk singer
Then Buford will soon starve to death