We have been getting this right from when we started the business.
When we first started at Rs 20 per trade they said they will not be able to survive as they will not make profits. It is 5+ years now, we have not only survived but are among the most profitable retail brokerage firms in India.
They said they will not be able to help you with anything - Zconnect, Tradingqna, and Varsity are probably the most popular online initiatives in India today. We are sharing knowledge much more than all traditional brokers combined.
They said since we charge so less, we will not be able to build on technology. Our product suite, especially Kite, Q, Quant, and Pi are today probably the best trading/reporting tools in India.
They said we will struggle to add clients without advertising, we have close to 2lk of them all through word of mouth and spending Rs 0 on advertising.
I can keep going on (remember I have vested interest 
). Coming back to your main question, the way exchange settles with the broker is exactly the same way, no matter if it is Zerodha, ICICI, Kotak or whoever else.
Every broker opens a bank account through the exchange called the client account. All broker client funds come into this and exchange credits/debits from this one pool. Exchange will not be able to ever directly reach out to a clients bank account, even if it is ICICI/Kotak etc who are banks.
So the question really to ask is, if a broker can close down. Yes, they can. But similar to how banks closed down in the US during the crash of 2008, banks can also close down in India. The important thing to note is that SEBI has done a wonderful job regulating Indian markets to ensure that retail investors are protected. Exchanges have setup investor protection fund which guarantees Rs 15lk per investor in case something goes wrong with the broker (remember no such guarantee for a bank account from RBI). The IPF is over Rs 1000 crores in size today and has never been used.
So yep, when a business can’t compete in terms of costs,technology, initiatives, support, transparency, they are bound to come up with a conspiracy theory. There is nothing that you need to be concerned about.