Here's some proof. One video per every popular modern pop artist.
http://www.youtube.com/watch?v=fD3J1kFkva8 Lady Gaga. "Born This Way" Acapella version.
http://www.youtube.com/watch?v=2bpAVvVwM5A Katy Perry. "Mannequin" Acoustic Version (She sounds a bit bad in the beginning, coz she's nervous, but it gets better.

http://www.youtube.com/watch?v=MFhBbsZSUfE Victoria Justice. "Make it in America" Live at Ellen Degenes Show.
http://www.youtube.com/watch?v=V2bt7qL7Uqc Rihanna. "Only Girl"&"S and M"
http://www.youtube.com/watch?v=tkuoRGig4Cs Bruno Mars. "Grenade" Acoustic Version.
http://www.youtube.com/watch?v=OC_74x-59uk Pink. "I Don't Believe You" Acoustic Version (my favorite performance out of the others on this topic ^.^)
http://www.youtube.com/watch?v=HEXHNUxD4tc Nicki Minaj "Moment For Life" On the Ellen DeGeneres show. She puts good style in her rap. Also, with the Chorus. She isn't lip synching. She's singing with the studio version. A lot of artists do that to find good pitch. Ususally, the studio version is played quiet.
http://www.youtube.com/watch?v=9p2zxZBnkw0 Selena Gomez. "Naturally" Acoustic version.
http://www.youtube.com/watch?v=0Qu8g7JuURY Justin Bieber "As Long As You Love Me" Acoustic Version. (the lyrics in my opinon are horrible, but he does hit some good notes, and does nice vocal tricks with his voice, which makes up a lot. Though, his songs of when he was younger, was better. Puberty kinda hit him hard)
http://www.youtube.com/watch?v=7_Wof32u1-Q Ke$ha "Goodbye" Studio Version. (I was surpised at Kesha. I didn't know she had this kind of vocal ability, and to even release her vocals like that, in a studio verison. Props to her)
http://www.youtube.com/watch?v=Tq8tK1rGpog Beyonce "Halo" Acoustic Version
I don't have a Brittney Spears video, because, her studio versions clearly show that she has amazing vocals. And, the only part of auto tune she uses, it the pitch correct, not the part where it makes you sound like you have vocal abilities.
And, the funny part is, the only live version i knew about myself, were the Lady Gaga and Katy Pery one. The other artists, only took my about 2-5 minutes to actually find the live performance. See how little time that is? For people to bother to look up a live performance to see if they can actually sing, rather than judge from the studio version.
Sorry if I don't have other major pop artists. If you like, you could mention the ones I don't have, and i'm sure I could find a good performance from them. ^_^