You could say that both are correct - there is no single knot which seems to be accepted as the definitive icicle hitch instead there are several knots which fulfil thie same purpose (some better than others).
I wouldn't surrender on this: there most certainly IS a definitive "Icicle Hitch",
as presented by John Smith (or was it Colin, of JM's knot?) in
Knotting Matters.
(And I believe the the OP has it right.) That is has been misrepresented here and
there, and adopted by arborists (in UK, at least) with load on both ends, shoudn't
change history.
Of that cited site's
The real strength of the icicle hitch is that it will securely grip a surface with the riding turns and can support a weight suspended upside down from a spar.
neither should "riding turns" change their stripes (and who's to say what's
upside-down--and why should
that matter at all to the knot?!).
--dl*
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