SWÍGA - to keep silent, to not speak

[009/25]

THAN SWÉON (SWÉGON?) THA FÜGELON
dan zwegen de vogels
then the birds kept silent

[132/19]

THACH HJA SWÍGATH THI .H.
doch ze spreken de <h> niet uit
but they don't pronounce the <h>

The German, Dutch and Frisian languages still have this word for not speaking, for keeping silent:
schweigen - german
zwijgen - dutch (IJ is pronounced just like EI)
swije - frisian

Older versions:
swīgon - oldsaxon
swigia - oldfrisian
swīgian, swīgan - oldenglish
swîghen - olddutch
svīa - oldnorse (to stop)

In the Scandinavian languages the word is more similar to the Latin version:
tie - norse, danish
tiga - swedish
þegja, þagna, hljóðna - icelandic
tacere - latin, italian
tăcea - romanian
se taire - french

Also different:
calar-se - portugese
callar(-se) - spanish

In old-Greek, the verb was: σιγάω (sigaō)
Noun: σιγή (sigé) - silence, quiet

It would make sense to relate the Oldgreek word to the German-Dutch-Frisian word, as most Dutch etymologists did, until recently (source):

J. Vercoullie (1925):
"Indogermaans *su̯ei̯k- of *su̯ei̯gh- + Grieks sigé (dat is *su̯ei̯gā) = het stilzwijgen"
"Indogermanic *su̯ei̯k- or *su̯ei̯gh- + Greek sigé (that is *su̯ei̯gā) = the silence/ not-speaking/ secrecy"

N. van Wijk (1936):
"Van een indogermaanse basis [...] waarvan grieks sīgé <het zwijgen>, sīgáō <ik zwijg>"
"From an indogermanic root [...] of which is derived the greek sīgé <the silence/ not-speaking>, sīgáō <I keep silent/ don't speak>"

J. de Vries (1971):
"Van deze wortel zijn afgeleid [o.a.] grieks sigáo <zwijgen>"
"Of this root are derived [a.o.] greek sigáo <to keep silent/ not speak>"

Van Veen & van der Sijs (1997):
"op enige afstand verwant met grieks sigaō"
"somewhat related to Greek sigaō"

But one of the newest etymological dictionary - M. Philippa e.a. (2009) - excludes this possibility:
"Verwantschap met Grieks sĩga 'zwijgend' is onmogelijk."
"Relationship with Greek sĩga 'silent' is impossible."

Why would it suddenly be "impossible" that the Greek <σιγ-; sig-> is related to the Germanic <swig->?

My guess is, because it would suggest that the Greek word is a degeneration (thus newer version) of the Germanic word.

Just like in Newfrisian it has lost the <G>: swije, in Greek it has lost the <W>.

And that would be against the ruling paradigm, in which Greek is supposed to be the older, more pure language.