The Chasidishe Hashgachos rely on the OU very often. So, if you turn down the OU, everything else comes along.
That is not exactly accurate. The Chasidishe hashgochos do not accept the OU hechsher for all products. They don’t accept them on certain OU foods that the OU allows certain kulos for, that they don’t accept.
So sometimes one can not rely on the OU for certain food products while relying on the OU for certain other food products, due to different kashrus standards.