Russell and Carol - hayle and hearty

I'm glad you realise it's a complete myth. Just to be super-clear, for the record:

There is precisely zero evidence to suggest that

1. Roman soldiers were ever paid in salt, or that
2. Roman soldiers were ever given a 'salt allowance'.

Both of these are outright fabrications, invented in the modern era.
Whether or not you personally happen to find either of them plausible,
there is no evidence whatsoever to suggest either of them.

What we're dealing with is a couple of vague ancient sources,
misinterpreted by an 18th century Latin dictionary, which was then
reinterpreted by 19th century Latin dictionaries. The 18th century
dictionary, Facciolati and Forcellini's Totius Latinitatis lexicon
('dictionary of the entire Latin language'), gave us version 1 of the
myth (Roman soldiers were paid in salt); the 19th century dictionaries,
including Freund, Scheller, and Lewis & Short, realised that that
was ridiculous and they reinterpreted it to give us version 2 of the
myth ('Roman soldiers got a salt allowance').

Here's what the 18th century dictionary says. The bit in bold is the key bit.

SALARIUS, a, um, di sale, ἁλώδης, ad sal pertinens. Liv. l. 29 c. 37. Vectigal etiam novum ex salaria annona constituerunt ... Salarius, ii, μισθοφορία, ὀψώνιον, stipendium, merces, annona, provvisione, stipendio, salario, mercede: proprie est annona salis, quae olim dabatur militibus. Plin. l. 31. c. 7. a med. Sal honoribus etiam, militiaeque interponitur, salariis inde dictis, magna apud antiquos auctoritate.

The bit in bold translates the noun salarius as:

strictly, the annual salt revenue, which was once given to soldiers.

The key word annona can mean either 'annual production' or 'annual revenue': swap it round, and you've got

strictly, the annual salt production, which was once given to soldiers.

Hey presto: version 1 of the myth.

The ancient sources in question are Livy 29.37.3, and Pliny Natural history 31.89 (§7 in an alternate paragraphing scheme). Livy is the source for the key word annona: he reports a tax on the annual salt production (salaria annona) which was imposed in 204 BCE. Pliny is the one who relates 'salary' to salt, as follows:

honoribus etiam militiaeque interponitur salariis inde dictis.

(Salt) is also related to magistracies and duty on campaign, and that’s where we get the word 'salaries'.

The Facciolati-Forcellini definition comes from taking Livy's salaria annona, swapping 'salt revenue' for 'salt production', combining it with Pliny's etymology of salarium, and interpreting his use of militiae '(duty) on military campaign' as encompassing the entirety of military pay.

In reality, nowhere near that amount of weight can be put on Pliny,
especially because it's obvious that he isn't reporting the devising of a
technical term but simply saying that he thinks two words are related.

As I said, 19th century lexicographers realised that Pliny's notion
couldn't carry anything like that amount of weight, but they still liked
the idea of soldiers' pay having something to do with salt. So here's
how Scheller's Ausführliches und möglichst vollständiges lateinisch-deutsch Lexicon (1804) presents it (col. 9655):

2) Salarium, scil. donum, eigentlich etwas Geld zu Salze, steht wie congiarium (s. Congiarium) ...

Salarium, that is, a gift: actually, after a fashion, 'money for salt'; by analogy with congiarium ('distribution of largesse').

Freund's Wörterbuch der lateinischen Sprache (1834) takes the same approach but makes it even more emphatic, and adds more analogies (p. 228):

C) salarium, ii, n. (sc. argentum, vgl. calcearium, congiarium, vestiarium etc.), ursprünglich der den Soldaten für Salz gegebene Gold, Salzsold, Salzdeputat ...

Salarium: that is, (salarium) argentum ('salt money'), cf. calcearium 'shoe allowance', congiarium 'distribution of largesse', vestiarium 'clothing allowance', etc. Originally the money that was given to soldiers for salt; salt-pay; salt-budget.

This was pretty much copied in Lewis & Short's A Latin dictionary, 1879 edition:

B. sălārĭum, ii, n. (sc. argentum; cf.: calcearium, congiarium, vestiarium, etc.); orig., the money given to the soldiers for salt, salt-money ...

Note that the 19th century dictionaries did not introduce any new evidence. They cite parallels like 'clothing allowance' to make their interpretation sound more plausible,
but they're still relying on the same bits of Livy and Pliny that
Facciolati-Forcellini did -- and as we saw earlier, they don't
substantiate anything of the kind.

But dictionaries are often taken as authorities, rather than tools. If Lewis & Short say that salarium
means 'salt-money', then by God it means 'salt-money'. Right? Right.
Well, assuming you're lazy and don't check the actual evidence, because
if you do, you quickly see that it's basically all made up.

Freund for germanophone readers, and Lewis & Short for anglophone
readers, set this meaning in stone for a century. At least one edition
of the Encyclopaedia Britannica copied it, and reinforced
version 1 of the myth at the same time, by juxtaposing it with a mention
of salt bars used to store value in modern Ethiopia (unknown date, vol. 19 p. 899):

Cakes of salt have been used as money, e.g., in Abyssinia and elsewhere in Africa, and in Tibet and adjoining parts ...

In the Roman army an allowance of salt was made to officers and men, from which in imperial times this salarium was converted into an allowance of money for salt.

Both versions of the myth in one place! The 1911 edition of the Britannica, for reference, includes the bit about 'Abyssinia' but omits any mention of Roman soldiers.

That omission does seem to reflect a 20th century awareness among
specialists that the 19th century dictionaries were talking bollocks.
But there wasn't another major Latin-English dictionary until the 1968 Oxford Latin dictionary. The OLD does get it right -- it says that salarium must be etymologically related to sal 'salt', but avoids making any guesses about how -- but by then the damage had been done.

More reading here in a piece I wrote nearly four years ago.

looking at the initial translation, my thought would have been that
the soldiers were paid out of some sort of tax on salt, or through
revenues generated from the empire's salt trade

It's only the 18th centry dictionary that claims that: that's
precisely the thing that was made up in the modern era. No ancient
source says anything like that.