The Times has asked the Twitter user to close the account, not because of sharing content but because of a trademark violation.
Eileen Murphy, a spokeswoman for the Times, said that not only is the paper well aware of the "holes" in its wall, but the holes have been left open intentionally.
"We have designed our digital subscription policy with the idea that we want it to have a porous wall. It is not a paywall in the typical sense of the word," she said. "We knew from the beginning that there would be people who would try to get around."
The Times wanted to continue to encourage an "open Web experience" and not cut off readers coming in from Twitter, Facebook and search engines, she said.
While some readers may continue to work around the paywall, the paper believes others will want the full, direct experience that comes with the monthly fee, she said.
"We fully expect that we'll have many people agree with that and buy digital subscriptions," she said.
But Search Engine Land's Sullivan said he takes issue with the paper's decision to block readers who come in from search engines and thinks other payment plans, such as micro-payments or a so-called "Hulu for news" might have been more effective in generating revenue while consistently limiting non-subscribers' access.
Still, given what he called the paper's "modest goals" for the subscription plan, he expects it to have relative success attracting digital subscribers.
"I've got no doubt that there are people who don't know or don't want to bother with the real simple things that can be done to get around it, and they'll pay for it," he said.