Ambiguity is present in all languages. Just as the referent of "them" in verse 7 is ambiguous in English, the Hebrew also allows several interpretations, although I think that the "scholars" mentioned in the question probably have the conclusion right.
Below is the text of the KJV with the transliterated Hebrew (BHS). The bold words are those in question. The three-letter roots in parentheses are the Hebrew roots behind the English words.
ʾimᵃrôt yhwh ʾᵃmārôt ṭᵉhōrôt
The words of the LORD are pure words
kesep ṣārûp baʿᵃlı̂l lāʾāreṣ
as silver refined in a furnace of earth
purified seven times
Thou shalt keep (šmr) them, O LORD
tiṣṣᵉrennûb min-haddôr zû lᵉʿôlām
thou shalt preserve (nṣr) them from this generation for ever
The OP asks whether them refers to words or something else.
Plausibility of disagreement
It is true that ʾămārôt ("words") in verse 6 is feminine, and the pronominal suffix -ēm in verse 71 is masculine. By "the rules", a pronoun should agree with its antecedent in number and gender, just as in most languages that mark nouns for gender. However, the exceptions in Hebrew are many. Most commonly an exception occurs when:
- a masculine pronoun is used for a grammatically feminine word, and/or
- the pronoun is in the form of a sufformative.2
Both conditions apply here. Thus, it is not out of the question that the suffix -ēm couldrefer to ʾămārôt in the previous verse.
On the other hand, the BHS apparatus (cf. NRSV, below) suggests an emendation toward the Septuagint (Greek), which uses a first person plural sufffixes on both verbs in this verse ("keep us... preserve us").
You, O LORD, will protect (šmr) us;
you will guard (nṣr) us from this generation forever
This relieves the somewhat awkward switch from plural to singular ("protect them....guard him"; the KJV has "pretended" that both are plural) and is morphologically conceivable.3
How to decide?
The decision about the referent in the personal pronoun may be best pondered by reference to your second question about the word "preserved" in very 7. Here we have two verbs in parallel with very similar meaning: šmr (KJV "keep") and nṣr (KJV "preserve"). One could ask whether words or people are the most likely objects of šmr and nṣr.
The first stich could go either way: words can be "kept" (e.g. Prov. 4:21), but Yahweh most often keeps people (Psalm. 16:1, 17:8, etc.). The second stich is more informative: the terminology nṣr + m- ("preserve from X ") is common, particularly in the Psalms (e.g. Psalm 140:1, 140:4, 12:7, 64:1, 32:7, 34:3). In every case as far as I can find, the one "preserved" is a person.
Although the lack of grammatical concord posed by the masculine endings in verse 7 is not insurmountable, the context makes it most likely that a person/people are in view as the objects of the two verbs. Whether to reach back to verse 5 for a referent ("they....him") or to adopt a fairly minor and plausible emendation ("us...us") is less certain to me. Either way, this does not support the KJV-only interpretation mentioned in the question.
1. Numbering is English[Hebrew].
2. Bruce K. Waltke and Michael P. O’Connor, An Introduction to Biblical Hebrew Syntax (Eisenbrauns, 1990), 108, 302.
3. rēm < rēnû by an enclitic mem (<hand-waving>) and assimilation of the nun (after some vocalization change); rennû < rēnû without any consonantal changes.