As someone who has bought all of those but one in the past 6 months... I call BS on the report. In Michigan, they run a background check at the gun shop while you finish filling out the paperwork. Total time is about 10 - 15 min. I provided them with my driver's licence and SS number (to simplify the background check)
When I upgraded to an iPhone this summer, it took 5 minutes.
When I bought beer on Monday night, it took 2 minutes... and I was carded.
When I bought a fishing licence, it would have been 2 minutes, but the 70 year old guy could not read my driver's license.
When I bought cold medicine, it took 2 minutes because they just had to record my driver's license number.
Buying a dog might be harder... but it should be.