The so-called chasidishe and very strict hashgochos all rely completely on OU supervision of their ingredients. Their supervision is that they rely on the OU and just make sure that the firm buys only OU ingredients. The OU’s level of supervision is unmatched by the others.
To say they completely rely on the OU is an overstatement. They rely on the OU when a particular product meets their own standards as well.
If it doesn’t, they don’t.