Here is how Modulus describes the legal issues. They also offer the ability to record streaming services.
"U.S. copyright law places restrictions on how DRM-protected content may be decrypted. The methods used inside Modulus to record streaming content does not include any decryption technology. The decryption is handled using the provider’s decryption technology as delivered to the user’s device from them directly. Modulus has developed a technique that intercepts the stream after it has been legally decrypted for a given valid user account. Thus, the challenges of stream recording in high definition are entirely technical in nature, not legal."
And
"The most relevant law is the Digital Millenium Copyright Act (DMCA). Specifically, Chapter 12 of Section 103 of the DMCA generated the most controversy relating to media content. It makes it illegal to circumvent technological measures (i.e. encryption) that control access to work (“access control”), when circumvention is the only or primary commercial purpose. While it is legal for a consumer to use circumvention to make personal copies of media he/she has rights to access, it is not legal to traffic in the circumvention software that enables it. MMS avoids this issue because MMS does not “traffic in any circumvention software” and furthermore provides no support for such software (the consumer makes that choice for their personal use after installing the unit).
Just as important, there are critical exemptions in the DMCA, including that copy-control circumvention (once access is authorized) is not prohibited. Also, the DMCA upholds the long-standing “Fair Use” doctrine permitting limited duplication of copyrighted material for personal use without requiring permission. Furthermore, the DMCA explicitly allows reverse-engineering of technological measures for the purpose of interoperability. This is the exact situation with the DVD and Blu-Ray libraries discussed above."
