I heard there were some restrictions on this, but that was decades ago. It could be reports that made it back to the US were inaccurate, or only reflected the policies of one or more province, or that things have changed over time.
A friend of mine, a preacher, who spent time teaching English in China said Three Self churches were kind of like Methodist churches. The house churches had different doctrine and did not want to join Three Self. A lot of them were Charismatic. Not all of course. Some of the Three Self people were not Charismatic and considered the house church's doctrine to be off, so some of them reported house churches to the authority, and that this has created a rift between the two movements. Also, some of the Three Self leaders early on, I read, held to 'liberal' theology, and some of those who went in the house church direction wanted leaders who held to the basic doctrines of the faith.
According to my friend, some of the Three Self people would think house churches are made up of heretics or Christians that are a bit off. And some of the house church people thought those who went to Three Self Churches were false Christians, persecutors of the church.
I have also heard of some of the Three Self congregations becoming Charismatic.
I hear that the government eventually allowed a great deal of freedom for the house churches-- which may not all meet in homes. 'House church' became the name for meetings that were not the Chinese version of the RCC or Three Self. Then, under Xi Jinping, in many provinces, the government began cracking down and hauling house church leaders off to jail, replacing crosses on walls with pictures of the president, etc.
Btw, 'Three Self' is an awful sounding name for a denomination, at least in English. It is also anachronistic, referring to some specific historical issues in missions. What do you call it in Chinese and what does it mean?