"Actually, Allen, that is only partially true. As a non-resident, you can legally purchase a rifle or shotgun (as long as you can pass the federal background check) and take it home with you that day"

Not if you're a resident of Illinois.

18 USC 922(a)(3) says it is unlawful for an unlicensed person (non-FFL) to transport into or receive in his state of residence any firearm obtained outside that state. There's an exception for firearms obtained in conformity with 922(b)(3).

922(b)(3) says an FFL may transfer a long gun to a non-resident if the "sale, delivery, and receipt fully comply with the legal conditions of sale in both such States" (transferee's state of residence and state where licensee's place of business is located).

Illinois requires a 24-hour waiting period for long guns. 720 ILCS 5/24-3(A)(g). Without the delay, the sale doesn't comply with Illinois law. The FFL is violating (b)(3) at transfer and the buyer is violating (a)(3) when he brings the gun into Illinois.