Well, that’s all right with me!
When I think of purely 70’s music it’s always the funk that comes to mind.
So I vote for the ultimate: Parliament - Tear the Roof off the Sucker
The most inappropriate song of the 70’s: Short People by Randy Newman.
True, but if you’re looking for songs that could only have been released during the 70s, disco is as good a place as any to look.
By the OP’s criterion (“if you played it to 1000 randomers the more who get that it’s from the '70s the more '70s it is”), you need a song that screams “70s!” not just to the people who were there, but also to the people who weren’t even born back then. And I think “Stayin’ Alive” is as good a choice as any.
The problem I have with “Stayin’ Alive” (or any other disco song) is that it doesn’t scream “70s!” It screams “Disco era!” which was two or three years of the 1970s. I have the same problem with Michael Jackson’s “Beat It” for the 1980s: it was in that era, and big in that era, but it was Michael Jackson’s sound, not anything you might call the 1980s sound. Same with disco.
Easy: “Theme from Shaft”.
Anyone offended by that has no sense of humour.
I guess I should start reading through these things before I post, shouldn’t I?
Okay. I’ll now go with “Papa Was a Rollin’ Stone”.
I think a lot depends on whether you were actually listening to music during the 70s.
In my head, “70s music” = disco. I know and love a lot of non-disco from that period, but in my brainspace it doesn’t exist as 70s music. It exists mostly as classic rock, which is an amorphous chunk of music that exists across, what, parts of three decades?
When you say “70s music,” I think “disco.” And when you say “disco,” I think “Stayin’ Alive.”
Just thought of another possibility: “New York Groove”.
Blue Swede’s cover of “Hooked on a Feeling”.
The Carpenters, Close to You.
I love 70’s rock. I am a somewhat reluctant Eagles fan. But I have to go with Hotel California also. Even without the iconic dueling guitar leads at the end, the song’s enduring popularity and lyrical meaning seals the deal.
My first thought was “I’d Really Love to See You Tonight” by England Dan and John Ford Coley.
Or “Baby Come Back” by Player.
But I think the best answer for me is the Bee Gee’s “How Deep is Your Love?” Because it’s so Bee Gees and so 70s “soft rock,” so it captures two huge parts of the 70s scene.
Interesting how the 70’s had several distinct genres: Disco, Soul/R&B, what is now defined as Classic Rock, but the 80’s genre was just “The 80’s.”
It’s too hard to settle on one song that defined the 70’s, but I think Stevie Wonder’s “Living for the City” satisfies the above genres to some degree.
No, no! You’re allowed to agree with me!
Although I suppose it may have been starting up at the end of the 70s, I think of “New Wave” as the most distinctly 80s genre.
No he isn’t! 
New Wave, and Hair Metal.