Optimal design choices for mosfet driver for DC-DC step-down converter
The first line in the LM27222 datasheet says 


  Adaptive Shoot-through Protection, 10ns dead time


...and at the bottom of page 6


  ADAPTIVE SHOOT-THROUGH PROTECTION
  The LM27222 prevents shoot-through power loss by ensuring that both the high- and low-side MOSFETs are not
  conducting at the same time. 


(more detailed explanations follow)

I would attribute your blown FETs to a scope probe slipping... it happens... (happened to me once). 

Blown FETs can have many other causes, for example bad layout:


Voltage spikes on switching (high supply inductance, bad decoupling...)
FET oscillation (too much grid inductance, long traces...)
Chip going nuts (lack of decoupling, etc)