Umm...not true. For context, I had my interview yesterday and they split us into 6 groups so that it would be easier for the interviewers to tackle us one group at a time. There were also tours and other things at the department and all in all, an extremely fun day.
I can't say the split between state schools and other schools in the other five groups but in my group, other than one or two people, everyone were from grammar schools (either free and extremely competitive or fee-paying) or were international students (European students).
They will not choose by schools - Imperial cares more about the merit of an applicant so you will be judged on your personal statement and other application related tidbits in addition to the admissions test you have completed.
You're probably going to ask this so I'm going to answer your question (preemptively anticipating that you will ask this): I applied on the 27th of September with 5 A*s in Maths Further Maths, CS, Chem and EPQ and I sat my admissions test on the 12th of October.
I have also applied to Cambridge (rejection from Gonville and Caius because of stupid admin mistake in TMUA ☹️ and because of the unprecedented popularity of CS applicants to that specific college), Durham (Absolutely no news so far but don't anticipate any news until March next year), Edinburgh (3 A*s with one needing to be in Maths and I got this within a couple of weeks of sending my application off and Manchester (3 A stars with one needing to be in Maths and two others in CS, Biology, Chemistry, Physics, Further Maths or Computer Science. If there is a practical component involved in my qualification, they expect me to achieve a Pass in that too. I got that within a week of sending my application off).
I will leave you with this final note: Imperial wants to take the best and only the best students for their course. There is a 1:20 ratio in places:applicants so they will be extremely stringent in choosing the best candidates. If you truly believe that you showed great merit in your application, and the university admissions tutors also mirror this thought, then why on earth will they not offer you an interview? THEY WANT THE BEST THEY CAN POSSIBLY GET IN A GIVEN YEAR.
Give it a bit of time. So far there have only been three sets of interviews that have been held (including mine) and there are many more to come. I know it's hard but try to relax and ignore anything. I tell you this advice because I was feeling the same for getting my Cambridge decision. I just really wanted to find out whether I really had got rejected or on the slim chance that I actually land a place at interview somehow (it would have been rather miraculous if it was the case), but after I got the rejection, I just felt dejected and a lack of motivation to do ANY work. All of that anticipation for nothing. Thankfully, I got the Imperial interview invite which then brought the fire back and so currently on the grind with schoolwork and I'm using it to distract me from the thought that I will get my decision within the next four weeks (in most cases).