Given that Green Eggs and Ham is a children's book originally written and published in English, in the United States, I'd say yeah, the meaning from your linked question is the same..
My point is that your question stems from a Spanish translation of American English poetry.
Dr. Seuss' poetry is well known for it's brevity in incessant repeating rhythms, and I'd say that using
¡Palabra! instead of
Te lo prometo as a translation for.
I could not, would not, eat them with a goat!
No podría ¡Palabra! comerlos con una cabra
Degraded down to
I could not, I tell you, eat them with a goat!
...is the best translation to use because
palabra rhymes best with
cabra in some unaccountable syllabic way.
To translate it literally would shatter the rhythm that the translator has created.
No podría !No lo haría! comerlos con una cabra
I guess it would work if you used an animal that ends in
To beat a dead horse, like Dr. Seuss.
Palabra = "I tell you, I say!" think Foghorn Leghorn :)
This usage shows up in RAE, if you're looking for solid research and not my ramblings.
Palabra. Interjección usada para garantizar la verdad de lo que se afirma.
(=interjection used to guarantee the truth of what is being asserted)