I can read the FAQ sheet, which says nothing about background checks, just keeping better tabs on these people once they are caught. If you want to read the actual text of the intiative, it says to download you have to enter your email. It doesn't give a choice just to view it, at least not that I can see.
I opened it without any problems.
And no, it doesn't state federal background checks as a recommendation.
The CDC handbook on how to set up a standards for employment screening does. It actually states that that a criminal background check will not catch people who have a predisposition toward child abuse unless you do a full federal background check and then you will not be able to weed out people who do not have actual credit or employment history if they have no such experience (they were specifically mentioning teenagers at pools).
I cant remember the name of the site I found the handbook in. I do know it was published in 1998, and was criticized as being outdated because the technology of many pedophiles has gotten to the point now where task forces are literally needed to do do background checks.
And you are right. background checks can be expensive, which is why they should be done by the government. Once someone has one it can be updated every three years and limit the costs. I do think there should be oversight on forcing employers to be burdened with those costs.
Many of these issues are addressed in advocacy sites on the internet. You just have to look for them. Sadly California is one of the slowest states in responding to human rights for juveniles.