That's pretty dead on but it's not really a prestige thing for Stanford since you can argue many of the schools in the top 10 are just as "prestigious" (few years back, Stanford was barely in the top 10).
The general rule for top, if not most, schools is that of the interviewed applicant pool, 30-40% get accepted (including off the waitlist) since their yield is ≤50% for the most part. The only real exceptions to that are Harvard (75% yield so <30% accepted post-interview IIRC) and UNC and UWashington (~80% yield each)*.
Of the interviewed applicant pool though, you have to remember that some people start withdrawing from schools at which they've already interviewed because they get into another school too so odds are actually better than 30-40%.
Either way, once you get an interview, you've got a great shot of getting in!
*Data is about 2 years old when I had a USNews subscription which gives all that info so I apologize that it's not up to date.