This is not exact for every situation, but is a good starting point.
If available, (some states do not disclose sales data), the primary source of sales data should be your county assessor office or which ever local government office compiles sales data.
The MLS and 3rd party websites should be used as verification sources and sources of information not found in assessment records.
Additional verification should be done by contacting a party to the transaction, such as buyer, seller, listing agent, or selling agent.
3rd party websites use IDX which should pull information from basically every MLS in the country.
3rd party websites are not replacements for the local Multiple Listing Service. However, if needed they theoretically should be "good enough" because MLS's use IDX to publish the information on 3rd party websites. When an agent outside of my local MLS sells a property, I get as much data as I can from assessment records and websites, then call the agent for verification and unknown information not listed on 3rd party websites.