My company used Zenefits for a while, mainly because one of our execs is friends with one of theirs. We had many, many problems with payroll. When you have employees repeatedly coming to you because their paychecks are screwed up, you've got to do something. We ended up switching away, and now use ADP for payroll instead. We've had no problems since. (This was before the big public slap fight between Zenefits and ADP, which was made even more amusing given our experience.)
I would not recommend anyone use Zenefits for any reason, regardless of whether it turns out they complied with legally-mandated training requirements or not. The fact that they were so incredibly sloppy is just inexcusable. You cannot mess around with people's pay like that.
(Posted with a throwaway account for hopefully obvious reasons.)