I give you that with very high motivation you can find out anything about anyone, more or less. I still think that the count of employers who would use such measures is miniscule compared to the count of employers who check felony records (because it's easy).
Additionally, according to this paper(1) around 8.6% of people have a felony conviction in the US. I have a hard time believing that all - or even most - of this felonies get reported by a newspaper/Google, so even for very noisy employers this seems to be a small risk (yes, if you are the "Slaughterer of <some town>" people will probably find you on Google even without a public felony record).
All else given: Start with removing access to felony convictions, then remove access to credit information and go from there. I didn't say it was easy, but at the moment the government (in the US) seems to do its best to make the life of people who have been convicted of a felony very hard.
Each company might not go through that on their own, but it will only be a matter of time until companies are started up whose business model is doing just that.
For $49.95 we will find any past convictions that any of your new hires might have!
Additionally, according to this paper(1) around 8.6% of people have a felony conviction in the US. I have a hard time believing that all - or even most - of this felonies get reported by a newspaper/Google, so even for very noisy employers this seems to be a small risk (yes, if you are the "Slaughterer of <some town>" people will probably find you on Google even without a public felony record).
All else given: Start with removing access to felony convictions, then remove access to credit information and go from there. I didn't say it was easy, but at the moment the government (in the US) seems to do its best to make the life of people who have been convicted of a felony very hard.
(1) http://paa2011.princeton.edu/papers/111687