web login cookie issue

There’s a newsletter website that I have a subscription to. I can login fine from Safari, but it does not work in DEVONthink. The site successfully logs me in … I know because if I type in a wrong password it gives me an error page … but then it acts like it doesn’t know I logged in.

I turned off cookies in Safari and then I got the same behavior in Safari. But I don’t understand. I thought that all WebKit applications literally share the same cookies and cookie settings.