Andrew Sihler (Sihler 1995) argues that Greek is "the only centum language [...] attesting a contrast between reflexes of ḱw and *kʷ". In Greek "two distinct sounds *ḱw give a double consonant medially, while the unitary *kʷ gives a single consonant" (p. 159). For example,
PIE *ḱw > Greek ππ, e.g. Greek ἵππος, Latin equus, equos, Myc. iqo
PIE *kʷ > Greek π, e.g. Greek ἕπομαι, Lat. sequitur
He also acknowledges the fact that this argumentation is based on one word only, Greek ἵππος, "whose peculiarities do not inspire confidence" (p. 160) [emphasis mine - Alex B.].
As for the contrast PIE *kw - PIE *kʷ, I think the evidence also comes from Greek (and Mycenaean): e.g. the so called boukolos rule states that "a labiovelar lost its labial element when adjacent to the vowel *u" (Fortson 2010: 70). For example,
Greek βουκόλος 'cowherd' (PIE *gʷoukʷolos > PIE *gʷoukolos), but αἰπόλος 'goatherd' (PIE*aikʷolos).
To conclude: PIE was not a monolithic, 'timeless' language that never changed. There is good reason to believe that there were different stages in its development, too.