可以。即：

The illegal vaccine ring was said to have been in operation since 2011.

=It was said that the illegal vaccine ring had been in operation since 2011.

两者在意义上没有什么区别，只是结构有所不同。又如：

It’s said that he stole the money.

=He is said to have stolen the money. 据说是他偷了这笔钱。

It’s said that there is plenty of oil off our coast.

=There is said to be plenty of oil off our coast. 据说我国沿海有大量的石油。