Here the printer’s manuscript has the nonstandard reading “them same words” while the 1830 edition has the standard “those same words”. 𝓞 is not extant here, so we cannot be sure how it read. The question is whether Oliver Cowdery might have replaced an original those with them or whether the 1830 typesetter might have changed them to those. There are three other cases in the text where the earliest text used the dialectal nonstandard them (rather than those or these) as the determiner for a noun:
For the two instances of “in them days” (found in the book of Helaman), the 1830 typesetter refrained from changing them to “in those days” (such editing occurred only later in the history of the text). But in the first example, the 1830 typesetter made the grammatical change of them to these (although those would have also been possible). Thus there is evidence that the 1830 typesetter could be responsible for introducing into the text the standard those here in 3 Nephi 19:8. On the other hand, we have no clear evidence of Oliver Cowdery replacing a standard these or those with them as the determiner for a noun. But there are two cases in 𝓟 where he replaced the standard those or these with them in the context of a following relative clause (the second of which was only momentary):
However, there were quite a few examples of them followed by a relative clause in the original text (see the brief discussion under 1 Nephi 1:20), so it is not surprising that Oliver might have accidentally introduced one into the text. But of greater importance here, the 1830 typesetter always set these instances of them followed by a relative clause. Only in later editing (chiefly by Joseph Smith for the 1837 edition) were instances of nonstandard them replaced with a standard determiner like those. But when we restrict the discussion to cases of them followed by a head noun, the minor evidence that we do have suggests that it would have been the 1830 typesetter who would have changed the nonstandard “them same words” to “those same words”. The critical text will therefore restore the nonstandard reading in 𝓟 for 3 Nephi 19:8.
Summary: Restore in 3 Nephi 19:8 the nonstandard them before same words, the reading of the printer’s manuscript; the standard those in the 1830 edition was most likely the result of editing on the part of the 1830 typesetter.