If I was in a vehicle accident, can a collision center get a copy of my accident report without me knowing and go to my house and convince me to take my vehicle to their shop?

Any report by law enforcement is subject to the Texas Open Records Act.  However, most law enforcement agencies will redact any confidential or identifying information.  Some will also redact contact information-- but this will depend on the agency.  So... to answer your question, it is possible for a collision center to get a copy of your accident report... however, it is up to you to decide whether or not you want to take the vehicle to their shop.  Before you decide to accept or reject their offer, call the agency who would have been responsible for the distribution of your report.  If they tell you that they did not distribute your accident report, you need to let them know that somehow, someone with their agency did release the report.  Your second step is to do a basic background search through the BBB or some other online consumer feedback group to determine if this is someone you want to use.  If a company is using "abulence chasing" techniques to get clients, it usually raises some serious flags about their business dealings.  This does not mean that all are bad-- just be careful and check them out thoroughly before engaging in any business dealings with someone you don't know.