In general, Stanford admits students who can be academically successful at Stanford without being “unreasonably stressful”, including admits with a ~27 ACT score. Stanford may not admit many students with this low test scores, but quite a few of them that do get admitted go on to do amazing things.
For example, in my opinion the most impressive and successful former CC poster I’ve heard of is probably MrTubbs, who is described at http://talk.collegeconfidential.com/parents-forum/425882-first-generation-urm-male-first-plan-messed-up-needs-your-help-p1.html . He received a 28 on his ACT and went to Stanford. At Stanford, he completed a coterminal masters with honors, interned at Google and The White House, was a Truman scholar and Rhodes runner up, started the The Phoenix Scholars which has helped hundreds of disadvantaged kids have similar college opportunities, received the highest award given to Stanford students (Dinkelspiel), become the youngest ever elected official of his home town during his graduation year, etc. He continues to make strides to improve his community today.
The lowest Stanford scores I’ve ever heard of were the ACT equivalent of a superscored 25/26 or non-superscored low 20s. She was also academically successful, finishing her bachelors+master in 4 years with honors. She describes her background and test scores at https://www.youtube.com/watch?v=k8fHUSgpMBg . While in Stanford, and beyond she also made amazing strides towards improving her community.
I received the ACT equivalent of a score in the high 20s, split up as 800M/500CR. I was a double-coterm (simultaneously working towards 2 masters + bachelors). I finished the bachelor + 1st masters in EE in slightly less than 4 years with above average grades while still having enough to be on sports teams (not a recruited athlete), have part time jobs, also do the pre-med track, etc. Later after graduating, I started a successful, small Internet company.
Obviously the low admits above are not common, but the point is I wouldn’t assume that you need a score with a certain relation to the student body to be academically successful. Or if you have a low score in relation to the student body, you’ll be stressed; and a high score, you won’t be challenged. Instead other application criteria have better correlations with academic success, and Stanford looks at these criteria when making admissions decisions.
Answering the OPs question, yes some students are admitted in that range; but being admitted is highly unlikely unless the rest of your application is very impressive, which cannot be gauged from the post…