amex and chase (one's i've talked to specifically about this but i'm sure others do as well) will auto-deny multiple apps because some people will apply for multiple cards when they only want one. One example scenario is people who don't have a great credit rating and want "a card" just to have the card so they can rent a car or whatever They apply for multiple cards hoping one gets approved.
For use churners/bonus-mongers, the key is to do the multiple apps at the same time (i.e., multiple browsers) so there's only 1 hard pull and then call the reconsideration line and do what it takes to get the multiple cards: yes, i want them all and yes i'll use them all; move credit around; cancel the old one (best if its age is lower than your average age) to get the new one, etc...
i've done 3 chase apps at the same time (3 browsers, switching between them to get them filled out and not have them timeout on me), been auto-denied on apps 2 & 3, waited a few days and then called in and got them all approved. And I've done it with Citi too, on the AA cards, come to think of it.
Don't know how they show up in my application history but i've never been denied a card for too many recent apps - which probably means i should apply for more cards....