You've never said exactly where you live, vchimpanzee, but I get the impression from your TV posts that it's somewhere in the rural area between Charlotte and Greensboro.
If you live in an area like that, the newspaper you receive from a neighboring large city is almost always going to be the first edition. Here's how the process works: most morning papers, even now, publish multiple editions. The early edition sometimes comes off the presses as early as 9 or 10 on the previous night if it's destined for readers at a considerable distance. It has to be that way if there's going to be time to get the paper printed and trucked to a distribution point and then distributed to the drop point where a carrier might pick it up to deliver it, or distributed to local newsstands in the distant towns.
(For instance, I live in Rochester, 350 miles or so from New York City. In order for us to have the New York Daily News and New York Post available on the newsstand by 6 or 7 in the morning, the papers we get have to be the earliest edition, and have to come off the press by 10 PM or so. The New York Times that we get here is printed in Buffalo, only 70 miles away, but it's the "National Edition" and also has an early deadline. We also get the early editions of the Buffalo News and of the Syracuse Post-Standard, at least on the days that Syracuse still prints a paper.)
Most papers then publish subsequent later editions, usually one for home-delivery subscribers in the metro area and a final edition for newsstand distribution in the metro area. I'm not sure where Fred gets his "3am deadline" information from; by 3 AM, most metro dailies are winding down their press run if they're going to get those papers on subscribers' doorsteps and newsstands by 5 AM. A more typical deadline to close the final edition of a morning paper these days is 12:30-1 AM.
If you're paying to get home delivery of the paper, you almost certainly have access to the "e-edition" of the paper, and that's generally the final edition with the latest news in it. If you want to "see what was said," that's the way to do it, and you don't have to go to a library.
The industry has changed dramatically in the years since Bush 41 was elected. Even then, afternoon papers were fading fast. There was a time when afternoon dailies were extremely important - before the nightly TV news and before the advent of hourly radio news, if you came home from work and wanted to know what had happened during the day, you depended on a home-delivered afternoon paper. Some of them included midday stock prices (and out west, the final editions of the afternoon dailies could even carry closing stock prices; I remember seeing the "late stocks edition" of the San Francisco Examiner being hawked on the street in the financial district there as late as the late 1980s.)
Today, of course, there are almost no metropolitan afternoon papers remaining, and the handful of small-town afternoon dailies that are still around tend to focus almost exclusively on local news, knowing that readers have already had plenty of opportunities to find out the previous day's national news from other sources. And many small and medium local dailies have closed down their own printing plants and now contract out for printing, which adds an additional layer of delay. Down the road from me, Gannett prints its Binghamton, Elmira and Ithaca papers at a single plant near Ithaca, which means there's an extra hour or so that has to be allotted to truck papers out to Binghamton and Elmira, even longer if the weather is bad and the roads are treacherous. Erie, Pennsylvania's Times-News is now printed in Butler, PA, nearly two hours away.
If you can still get daily home delivery of a paper that comes from 60 miles away or more, you're lucky. The cost of distribution and delivery has led many papers to curtail their print delivery areas pretty substantially. I used to be able to walk around the corner and get daily apers from Boston, Toronto, Albany and beyond. Those days are over, and I'm pretty lucky to still be able to get the New York and Buffalo papers here. As I noted above, Syracuse doesn't even have a daily paper anymore, and it's about to be joined by Cleveland and very possibly Newark, N.J.
Like it or not - and I know you're a little leery of technology - if you're in an area that's distant from a major city and you want daily news from that city, the future is all in electronic delivery.