The Asset Management Company (AMC) run by SBI is regulated but the Securities and Exchange Board of India (SEBI). The Mutual Fund industry is quite tightly regulated by the SEBI – there is a separate custodian, a registrar and then the AMC itself. They are regularly audited as well.
That doesn’t mean that there is no room or mischief. There is always the risk of the fund underperforming the peer group. Hence you need to track the funds closely or appoint an advisor (SEBI Regd) who does this for you. Invest in direct plan mutual funds so that brokers are out. Much industry mischief is through incentives to brokers.
Having said that many SBI funds are performing reasonably well. There is on reason to jettison any of them now.