I agree that this is the implication of the passage. I gathered six references from ancient literary sources in this thread, with some notes on critical method:
http://slinging.org/forum/YaBB.pl?num=1407020188(page 4 also gathers some visual evidence)
and I repeat them here. Most of them are, in fact, from Latin literature, so you may want to decide how relevant they are. The internet search engines for all of Greek literature give you about 500 occurrences of σφενδονή, sling, and cognates; of course, you have to add paraphrases, etc.
Literary evidence
There are only two I know of. They are later than the period we're talking about.
1. Virgil, Aen. 9.558.
stridentem fundam positis Mezentius hastis
ipse ter adducta circum caput egit habena
et media aduersi liquefacto tempora plumbo
diffidit
Mezentius lays down his spears, and thrice around his head drives the buzzing sling
with taut thong, and with molten lead splits the forehead of his foe,
It describes 3 rotations above the head, slinging lead. Problem: it's in an epic poem, which describes lots of things, some quite exaggerated. . But precision and realism might be aimed for here, in contrast with the more outré fighting scenes
2.Vegetius 2.23
Adsuescendum est etiam, ut semel tantum funda circa caput rotetur, cum ex ea emittitur saxum.
The habit should be given, to spin the sling only once around the head, when it is used to throw a stone.
The same adverb, "around", being used in both passages, helo. or abbreviated helo. is being described here, since "three times" must describe multiple rotations, with a low rotor. This can be considered absolutely certain, on linguistic grounds.
and
3
Re: How did the ancient sling ?
Reply #81 - Sep 7th, 2014 at 7:40pm In the treatise on Mechanics attributed to Aristotle (but certainly not by him), the question is raised-- why do projectiles fly further from the sling than when thrown by hand ?
One of the explanations is
ὅτι ἐν μὲν τῇ σφενδόνῃ κινούμενον τὸ
βέλος ῥίπτει ὁ βάλλων (περιαγαγὼν γὰρ κύκλῳ πολλά-
κις ἀφίησιν), ἐκ δὲ τῆς χειρὸς ἀπὸ τῆς ἠρεμίας ἡ ἀρχή·
(852A)
"because the thrower throws with the sling a projectile in motion (for he looses it having led it round in a circle many times), but by hand from an immobile starting point"
Perhaps Archytas of Tarentum, late C5th BCE (Thomas Winter); perhaps much later, e.g. C3rd BCE. Anyway, the earliest description of the movement of a sling, by a natural philosopher.
http://en.wikipedia.org/wiki/Mechanics_(Aristotle)
4. From the lexicon of Pollux (Roman era work on Classical Greek usage). 1.175
ἐρεῖς δὲ τὰς σφενδόνας πληρώσασθαι, τὰς σφενδόνας στρέψαι, (5)
τὰς σφενδόνας ἐναγκυλίσασθαι
You can also say "fill your slings", "twist / spin/ turn your slings", and "fit your slings to their thongs / 'thong' your slings'.
No idea what the third one means. It reads like military orders.
5.Another reference, Silius Italicus 1.314ff
hic crebram fundit Baliari uerbere glandem
terque leui ducta circum caput altus habena 315
permissum uentis a<b>scondit in aera telum,
One hurled volleys of bullets with Balearic sling: standing erect, he brandished the light thong thrice round his head, and launched his missile in the air, for the winds to carry
It's a poet, writing about Hannibal in the first century CE. Like Virgil, he believes that three rotations around the head is the way to go
6. Vegetius, 3.14
Funditores sunt qui fundis lino uel saetis factis - has enim dicunt esse meliores - contorto circa caput brachio dirigunt saxa.
Slingers are those who throw stones with slings made of linen or coarse hair (the latter are said to be the best) by turning / twisting their arm around the head.
(For me, this, again, is about revolutions around the head, i.e helo style).
[edited to add in the actual figure for occurences of slinging in Greek literature-- I had to check]