Can you copyright data in any way?

The answer is that I think it depends on the data. An compilation of sales statistics with an original analysis and complex extrapolations? Probably. A compilation of sales statistics with no analysis? Probably not. A table of baseball stats, Wall Street stats, or other data from publicly available sources? Definitely not.

A compilation of data can have sufficient creativity to be registrable, which is what I interpret you to be asking. "Certain data" may or may not be separately copyrightable, but likely the manner in which it is displayed is. And, as you apparently did, you can contractually agree not to do something. The terms of your subscription are something to which you contractually agreed. There is a good bit of litigation on this stuff revolving around a "sweat of the brow" guideline that long existed. It has been to the Supreme Court. [Google Feist Publications, Inc. v. Rural Tel. Serv. Co.,499 U.S. 340 (1991).] and review the extensive discussion from the US Copyright Office on the matter.

One of the requirements for a copyright is that the work be sufficiently original. This threshold requirement of originality is not met by simple raw facts. For example, the telephone numbers are not, by themselves, subject to copyright protection. But the organization in a compilation of such data in the yellow pages may be sufficiently original to qualify for copyright protection. Under the Copyright Act, a compilation is a "collection and assembling of preexisting materials or of data that are selected in such a way that the resulting work as a whole constitutes an original work of authorship." 17. U.S.C. § 101. In Feist Publications v. Rural Telephone Service Company, the U.S. Supreme Court held that a compilation work must contain a minimum level of creativity in order to qualify for copyright protection. In addition to the copyright issue, there also may be a contractual issue in your subscription example.