If you have a lot of inquiries, I am betting on that as the possible reason for the decline, not so much any other information. With regular credit, inquiries on your report don't matter as much as they used to. But with chexsystems they do.. a lot. Opening, or the appearance of opening - or attempting to .. sends red flags that you might be doing something irregular. Rather then take the chance, they decline you.
There are inquiries I have seen on my report from companies other than banks, duplicates, etc. I disputed most all of my inquiries as "NO PERMISSIBLE PURPOSE".. meaning that I did not authorize the banks to run inquiries whenever they felt like it.. and with this alone, they were dropped. Get the inquiries off you report, and try and open your account again.
Your Lexis report.. prepare for it.. it will be thick. Lots of information that sometimes parrots the credit bureaus, sometimes not.
I just send out a week ago nearly 50 individual letters to every credit place I could find requesting my reports. Its worth the time and postage to be in control of your own information.
At the end of the day, you will be an informed consumer and will be able to dictate your information.