How far back can a company find DUIs?

The company that I am going to be training for states that you can have,

• No DUI or DWI violations in the last 5 years
  
• No more than 1 DUI in the last 15 years
  
• No more than 2 DUI’s in your lifetime."
  

If DUIs drop off of your DMV printout, is it possible that a company can find old DUIs?

My last DUI conviction was over 22 years ago. Don't ask me how many I had total before that conviction. Just be aware that my LAST DUI was over 22 years ago.