Most KIA lines are best thought of as arising from 1 Nf3, I agree, but a few aren't. And with (anti-)French lines, for example, I guess you could make arguments both ways. Does the table below (showing most of the 'Reversed' lines first) help?
*****
King’s Indian Attack: Defences
Reversed KID, Classical [KID Reversed]
Reversed KID, Seirawan System [Karpov System]
Reversed KID, e3/Nf3 [‘Main Line’ (A08)]
Reversed KID, main-line Fianchetto [KID Reversed]
Reversed KID, Fianchetto with e3/Ne2 [Kasparov System]
Reversed King’s Indian Attack
Reversed English, Closed (Nc3/Nf3/g3/Bg2/d3)
Reversed English, Botvinnik System (Nc3/Ne2/g3/Bg2/e4)
Reversed English, Bremen System (Nc3/Ne2/g3/Bg2/e3)
Reversed English ((Nc3)/Nf3/e3/Be2)
Reversed English (Nc3/Nf3/e4/Be2) [Czech Benoni line (A04/B30)]
Reversed Pirc, Classical
Reversed Pirc, Fianchetto with Nf3
Reversed Pirc, Fianchetto with Ne2 [Pachman Variation]
Reversed Pirc, Dolmatov System [Dolmatov System]
Reversed Torre Attack [Keres System]
Reversed London System [Lasker System]
+++++
Caro-Kann/KIA (A04), 1 e4 c6 2 d3 e5 3 Nf3 d6 4 g3 g6 5 Bg2 Bg7 6 0-0 Ne7
Caro-Kann/KIA (A05), 1 e4 c6 2 d3 e5 3 Nf3 d6 4 g3 g6 5 Bg2 Bg7 6 0-0 Nf6
Caro-Kann/Petroff (C42), 1 e4 c6 2 d3 e5 3 Nf3 d6 4 g3 Nf6 5 Bg2 Be7
French/Reversed Philidor, 1 e4 e6 2 d3 d5 3 Nd2 Nc6 4 Ngf3 Nc6 (C00)
French/Reversed Philidor, 1 e4 e6 2 d3 d5 3 Nd2 Nf6 4 Ngf3 (4 g3) b6 (C00)
Hedgehog (...c5/…b6/…e6) (A04)
Hedgehog (...c5/…b6/…g6) (A04)
Queen’s Indian Defence line (…b6/…e6 [RR …c5]) (A05)
Spassky Variation (A05)
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