I would say petty theft is absolutely less common in Japan and I will leave my laptop in a starbucks while I go to the toilet or go to order something which I wouldn't in Europe or the US for example.
However, I have seen crime in Japan, a close Japanese friend of my non-japanese ex-wife stole her bankbook and proceeded to withdraw money (my ex-wife used the same pin for her phone and her bankbook and so her friend most likely saw the pin from the phone). My ex-wife reported it to the police, the "friend" gave the money back and got a slap on the wrist but no real consequences.
My female roommate also had a lot of experiences of various sexual crimes, over the 7 years she lived in Japan, her underwear were stolen once, she saw a flasher who was completely naked under his coat and opened it when she passed by and she was concerned enough by someone following her over multiple blocks that she went to the koban.
And finally, as a male, I once went to the urinals in the toilet in osaka and noticed the guy to my right making noises, he was looking at me and touching himself... Kind of turned me off for years of public toilets.
So, the myth of Japan being crimeless at least to me seems like a myth. Crime takes different form, sexual crimes are definitely in my anecdotal experience more common than in other countries, theft of belongings are definitely less of an issue than in Europe/US.
Also, I don't think any of the above crimes would show up in statistics. I'm pretty sure the first one which was straight theft would not have been reported at all.
However, as a counterpoint to reporting, my ex-wife knew of a foreign student at her university who stole for a bit more than 1,000 jpy of things from a combini, was deported and not allowed to enter Japan for 5 years. I'm pretty sure that any crime committed by foreigners in Japan will always be reported and treated harshly.