What are they going to train them to recognize?
The Form 4473 you fill out when purchasing a firearm asks the buyer if they are the actual buyer of the firearm. However, even if you are buying a firearm with your own money as a gift, you are considered the actual buyer. It is only if someone else gives you the money to buy the firearm that you become a straw purchaser.
See question 12a on page 1 and notice 1 on page 3.
http://www.atf.gov/forms/4473/
The typical scenario I've heard gun control advocates describe is two people coming into the store. The first person looks at the gun, handles it, and finds what they like, but when it come time to purchase the gun, the second person fills out the paperwork and pays for the gun.
Despite what the media and gun control advocates would have you believe that is not illegal unless the first person is actually providing the money to purchase the firearm or paying them back later.
The person who purchases the firearm and therefore takes possession of it from the dealer has to fill out the paperwork.
The dealer is responsible to make sure the person who purchases the gun can legally do so. If they see one person give another person money with which to purchase a gun, then they should probably refuse to sell them the gun. Although even then if the one person is simply loaning a friend the money with which he is purchasing the gun, it is still legal, as long as he isn't purchasing it for the person who "loaned" him the money.
Logic sometimes escapes the legal process.
The government has held bartenders liable for diagnosing who has had too much to drink for a long time now.