World's Safest!  Wow, that's quite a claim!
Yes it is.  To understand the Safety benefits of the SettleSafe crib system, it helps to define two key concepts: System Safety and Unintended Handling

A system includes not only the product or the process but also the influences that the surrounding environment (including human interaction) may have on safety performance.
So how does that apply here?

The crib is the centerpiece of the baby sleep process.  So measuring crib safety should include all human interactions related to baby sleep.  If baby finds the crib to be uncomfortable or isolating, then excessive lifting and handling will be needed at sleep time.  Ideally, handling of baby at sleep time should be limited to placing her down in the crib, and then lifting her out only at the end of a restful sleep - or perhaps for feeding or changing.

Any unintended handling or lifting introduces the opportunity for injury and compromises the safety of the sleep system.
Why is lifting and handling a hazard?

The SettleSafe crib reduces or eliminates Unintended Handling.  This makes it the Safest Baby Sleep System in the world.
Infant Injuries 2
According to Hawley et al, 83.5% of infant injuries requiring hospitization are caused by falls, including drops?
Infant Injuries 1
Brown et al, included injuries not requiring hospitalization and found that 55% of all infant injuries resulted from falls
We all may recognize one or more of the high-risk handlers:

Sleepy parent who may settle with baby in a nearby chair, sofa, or bed.
In the Safety section of their 2016 review of Baby Cribs, Consumer Reports lists the main decision criteria as 1) Simple Design, 2) Quality of Construction, 3) Professional Assembly.

That means not a single crib on the market had an innovative safety feature worth mentioning.
Current Crib Market
First, some boilerplate from Wikipedia: