(We have a blog post on the topic here)
The CEC only accredits individual installers (the actual person). It does not accredit companies and never has. All installers (the individuals) must be accredited. All the installers who are employed by the top ten are accredited. You can ask them for their ID to prove it when they come to install.
Companies who employ accredited installers often display the "CEC Accredited" badge, adding to the confusion.
Any solar company can join the CEC as a member if they pay a few thousand a year. These companies can use the "CEC member" badge on their website.
In the last few months the CEC has launched a 3rd scheme called the 'Approved Solar Retailer'
As you can see, not many companies are approved yet as it is quite a lot of hoops to jump through. Those that are in the scheme can display the 'CEC approved retailer' badge!
If an installer (the person) performs a substandard install, you can complain - if it is serious he/she could get their accreditation (and possibly their electrical licence) revoked.
You are covered by Australian Consumer Law, and the Australian Standards if the work is not to standard.
And if a solar company in the SolarQuotes network does a bad job, they get a phone call from me which usually results in a quick resolution! Thankfully I don't have to do this very often!