This is easy to explain from a business point of view, although difficult to explain from a logical point of view.
Print eyeballs are about 10 times more valuable [publishing2.com] than digital eyeballs.
Therefore the main concern is expanding print subscribers.
One way to do that is to offer digital previews that are effectively teasers to entice users to get the print edition. In order to ensure that you get the print edition, and not the digital edition, they charge more for digital alone than for digital + print. Note that the NYT has no problem if you only access their content online. There are no "print monitors" that track which printed articles have been read. As far as the NYT is concerned, you can burn the print paper as soon as it hits your door, as they will get paid by the subscription numbers. So the NYT has a single goal -- to sell more print editions, but the consumers of the NYT want the easiest access to NYT times data, which may be online. The solution is to require the purchase of a print edition in order to access the data online, and to discourage customers from only accessing the data online.
Underlying all of this is a very broken business model on the part of the paper as well as on the part of advertising companies. We have much more data about online advertising than other forms of advertising, and this data describes how ineffective digital advertising is. But instead of assuming that this applies to all forms of advertising, through sheer inertia, advertisers have determined that this is an odd quirk of online advertising only, which means all other forms of advertising, for which we have less reliable data, continue to be able to command a premium over online advertising.
All of this is a detriment to the development of rich content online sites, and a subsidy to tree and television based sites.
By the way, Hulu faces the same problem with obtaining add revenues for shows online versus the add revenues that networks can charge. This is why the networks would rather you watch a show on television than watch the same show online. They use the online shows as a teaser or advertisement for the on-air shows, doing things such as delaying programs or limiting the availability of programs while giving the online audience a sample of their content.