You fill it out (and sign it the first time) on the first day. After the wait and the NICS check, you sign again certifying that all your previous statements are still valid. THEN you can take delivery.
Correct me if I am wrong, but my understanding it he was also not legal to won the rifle based on his address, if he lives in Chicago he cannot buy a gun that is illegal for him to own.
Now if he was not convicted of domestic violent, which it would appear he never was (did a quick BING search, he would be O.K to own the rifle), but if he was an alcoholic issue then he would be illegal.
One interesting thing I have seen with folks who think guns should be illegal: a great many of them have problems with impulse control, as such they project that every one has a similar issue. So to them the idea of folks having a gun is scary, as thy know they could not handle that responsibility, and so when they speak of the fear of folks with arms they assume every one thinks like them.
Likewise folks who grew up in the gun culture cannot understand that, as we have always had self control and come from family lines that have a high degree of self control.