I think they use "trinary" in the Camel book because most English speakers can immediately grasp the meaning of the word, especially when it is listed alongside "unary" and "binary".

The prefix tern- came into English from Latin, via Old (Norman) French. The prefix tr(e)i- is a direct borrowing (by scientists) from Latin or Greek.

This is excerpted from the Oxford English Dictionary, 2nd Ed.:

trinary, a. and n. rare.
ad. late L. trinari-us of three kinds (Isidore Orig. iii. vi): cf. L. ternarius ternary.
A. adj. Consisting or composed of a set of three; threefold; triple; ternary.
1474 Caxton Chesse iv. ii. (1883) 166 For the trynary nombre conteyneth iii parties whiche make a perfect nombre.
1884 M. Boole in Athenĉum 23 Aug. 238/1 Ascribing to the Eternal a dividedness projected from the trinary nature of the human faculties.

ternary, a. and n.
ad. late L. ternarius consisting of three, f. tern-: see ternal and -ary1. Cf. F. ternaire (15th c.).
A. adj.
1. a. Pertaining to, consisting of, compounded of, or characterized by a set (or sets) of three; threefold, triple. ternary system (of classification), one in which each division is into three parts.
1430 Art Nombryng 19 Some vsen forto distingue the nombre by threes, and ay begynne forto wirche vndre the first of the last ternary other uncomplete nombre.
1909 Cent. Dict. Suppl. s.v. Symmetry, If (the angle is) 120°, or the crystal repeats itself three times, the symmetry is threefold or ternary and the axis is a triad axis.

40 years isn't a lot of time in the history of English. I'd say it's just misplaced snobbism.

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Allolex