I am not sure if I agree with this. Ven. Ñanānanda is presumably saying that if one form of the word “to be” (in this case the past participle bhūta) means “become”, then other forms of the same root must have the same meaning. This would mean that the verbs bhavati and hoti must always be translated as “to become”, which is simply not possible. In most contexts bhavati and hoti mean “to be”. The same applies to bhava, and its meaning can therefore not be fixed by the meaning of bhūta in this way.
The word bhūta itself does not always mean “become”. In certain contexts (e.g. DN 15) it refers to a class of beings, and in this case the meaning would seem to be closer to “existence” than “become”. This shows us once again that words acquire meaning from their usage in a particular context, and that it can be misleading to derive meaning on theoretical grounds.
And why not? It seems to me that re-existence makes eminent sense in this context, whereas re-becoming verges on the incomprehensible, as Bhante Sujato has argued here.