The problem with the above argument is that it's basically a comparison statement without clearly stating the comparison. What is really being claimed is that house churches are in more danger of falling into doctrinal problems than are traditional churches.
My question in response is simply, "What evidence is there for the claim that house churches are in more danger than traditional churches of having doctrinal problems?"
My guess is that some people who do not like and/or are not comfortable with the house church movement have heard of some house churches that have had doctrinal problems. I don't doubt that the problems exist. When we look in the New Testament in particular, we see many warnings about the problem of false doctrine. It is a sad reality.
The problem with the above strawman argument is that traditional churches also sometimes have doctrinal problems. As with house churches, this often happens when someone with a forceful, charismatic personality starts teaching false doctrine and leads others astray.
This can occur in house churches and it can happen in traditional churches.
One benefit of house churches is that everyone gets to participate in doctrinal discussions. The elders/pastors do not dominate the conversations. Therefore, there are more voices involved to act as a check-and-balance against any false teaching. Since no one person is elevated as the primary teacher, people are less likely to follow that teacher into falsehood if he strays in that direction.
In the traditional church, everything is doctrinally fine as long as the elders/pastors remain solid. We can be thankful that this is usually the case. However, if the pastors begin teaching falsely, many people are likely to follow them down that dangerous path.
Regardless of what type of church we are a part of, we must all be vigilant in our stance against false doctrine.
To summarize: Is it correct to say that house churches sometimes have doctrinal problems? The answer is yes. Is it correct to say that house churches are in more danger than traditional churches of having doctrinal problems? The answer is no. In fact, I'd like to challenge anyone to provide data to show otherwise.
Additionally, the model of the house church actually acts against false doctrine because no one person is elevated to a position where he will be able to easily lead others astray.
In the end, the argument that house churches more easily fall into false doctrine is simply false.