You say "beide" in front of people, animals or objects. However, if you refer back to something you mentioned earlier you need to use "beiden" for people.
- Beide kinderen eten een appel (Both children eat an apple)
- Beide paarden eten een appel (Both horses eat an apple)
- De kinderen eten beiden een appel (the children both eat an apple)
- De paarden eten beide een appel (the horses both eat an apple)
It's very good english in itself. And it carries exactly the same information. Could be there's a version in dutch that's both idiomatic and identical to this english, and thus not considered the best translation for the Dutch.
I find it a bit silly that we have to guess at what else exists in Dutch (that we have not yet learned) to know what latitude we have in the English translations, though.
Basically, if "Beide dieren hebben een blauwe tong" is good Dutch too, then we can't use the translation you suggest for "Beide dieren hebben blauwe tongen." If it's not acceptable, then we can.
That's sort of like having to apply Bayesian statistics to our answers. (Or omniscience.) Seems like there should be a better rule for "close enough" that does not presume near-infinite prior knowledge.