I bit and was approved for the card via the online chat after the screen that said the application had been received. They said they had to verify some stuff, but essentially the only thing they verified was to ask me if $xxxx is sufficient for me for a credit line and I said yes, because as long as I could charge $1000 in a shot to get my $250 I was fine and the line they were offering was well above that.
Regarding the $300 max, I did see in another thread that the person had written to Citi to ask if sign-up bonuses are included in that cap, and the response was that it's not included.