I worked as a research assistant in adolescent medicine in college. My gut told me the first statement wasn't even true.
Here's a large study of adolescent stealing behaviors.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3671850/#!po=1.19048

Demographics of the sample are presented (Table 1). The overall prevalence of stealing was 15.2% (95%CI: 14.8–17.0). Twenty-nine students (0.72% of the entire sample, 4.6% of those who steal) endorsed stealing symptoms consistent with a DSM-IV diagnosis of kleptomania. Males were more likely to have reported stealing than were girls. African-Americans and Asian-Americans were more likely to have reported stealing. Those students in 9th grade were more likely to have stolen, and students living with two parents were less likely to have stolen (Table 1).

It's self reported, which can be a rub if boys are more willing to admit to behaviors they see as masculine/ adventurous, and girls less so if they've internalized that the same behavior is "trashy"/ unfeminine. But n=3999 and it apparently tracks with other studies with differing methodologies. Kids are pretty honest about behaviors on surveys, actually, as a general rule.

If anyone is wondering, girls made up a smaller percentage of those in the "kleptomania- qualifying" group too.

So maybe boys are more likely to go through a stealing thing because their ancestors had to provide for their mates during/ after pregnancies. Just spit balling here.

[Anyone else find it weird that they write males in the bolded sentence and then girls?]