Yes, Using a DVR to Record OTA TV is Legal in the U.S. It's Not A Form Of Piracy.
Here's some context: The allotment of radio frequencies OTA broadcasts use is considered the public airwaves in the United States. The entire point for these broadcasts to exist is for them to be seen by the American people. The Federal Government gives free access to these radio frequencies via license agrerements to broadcasters with the condition that they provide at least 1 free TV channel operating 24/7, 7 days a week, with certain other restrictions to ensure their operations meet public interest obligations. This is discussed in detail at fcc.gov
Even broadcasters themselves, like the E.W. Scripps Company with Tablo, make network connected DVRs that are made for consumers to record free OTA TV broadcasts.
The Definitive Legal Basis Is Based On A Supreme Court Case:
Sony Corp. of America v. Universal City Studios, Inc.
In this case, The Supreme Court of the United States ruled that the making of individual copies of complete television shows for purposes of time shifting does not constitute copyright infringement, but is fair use.
Broadcasts are in the air, everywhere, and free. My recommendation for everyone using a OTA DVR is to only share recordings with individuals in their household. The great thing about OTA TV is that it's so ubiquitous: friends and extended family can set up their own DVRs and record programs themselves!