Thanks for reaching out.
One thing is certain: a strong referral increases your rates of getting a positive screening outcome and geeting an interviews.
However, this is not a must at all!
If you have a strong CV with achievements and a great profile, you will get interviews, no matter what office you are applying too. Do not get disturbed by the noise on social media. I got all 90% of my interviews with 0 referrals and it went just fine.
The process is very standardized and the HR and consultants screen the CV based on your profile.
That being said, if you do not come from "a target school", getting a referral is the best way to get interviews. That's just the way it works, not necessary, but strongly recommended.
Also, it's great to network with people from the office you are applying to in order to get a sense of the job they are doing and the atmosphere and values they have.
Best of luck in your applications, and do not hesitate to reach out by PM if you have any questions,