Not an expert, but in the U.S. making a copy of a broadcast for personal use is legal under fair-use. Anything that loads up on your computer screen you can make a copy and save it for personal use. So screen captures are by definition legal.
How exactly you copy the material on your screen gets tricky under the DMCA clusterfuck. Breaking encryption to copy the material is illegal unless there is an valid exception for fair-use. What exactly those valid exceptions are is above my paygrade.
Terms and conditions are NOT copyright law. They are a separate agreement that is the companies “wishlist” of things they want the consumer to agree too. It’s common for them to spell out terms in direct conflict with copyright law.
The reason that an iTunes video purchase is encrypted is because it is illegal to break the encryption in order to make a copy (DMCA). However capturing the playback and transforming it to another medium is for personal use is fair-use.
There is also no time limit to how long a person can save the copy for. As long as they had legal access to the content at the time of making the copy. For example say I recorded a football game from a streaming service. I can save that copy for personal use for the rest of my life even though I purchased a one time only streaming.