Say, I pay for a broadcasting service, and lets say due some circumstances I miss it.
Does the original copyright (or the fact that it allowed me to watch it), allow me to source the content elsewhere?
I in no way am sharing the content that was aquired elsewhere.
Edit: Likely I will watch it one time and delete it afterwards.
Edit: I know the alternative source is infringing copyright. But does that have any effect on me?
This is not a copyright issue as you are not making a copy (save for a transient one in your cache which is allowed). You are allowed to record it for personal time-shifting as that is fair use/dealing.
The broadcaster either owns the copyright (unlikely) or has a contract with the copyright holder that allows them to broadcast it. Assuming the broadcaster chooses or is not permitted to subsequently stream it, if you miss it, you miss it. Your contract with the broadcaster is over. Their obligation was to make the broadcast available to you, yours was to pay for it - nobody is obliged to watch it.
You can, of course, seek the content from any other legal sources, complying with their terms including payment if necessary.
No, you may not legally get the content elsewhere: that is a violation of copyright law. When I create content that I want money for, I negotiate with a distributor such as TW, and I grant TW a license to make my stuff available. The license can have all sorts of terms in it, for example conditions on where and when it can be distributed, and how much TW must pay me per user. Such content usually has some requirement of keeping track of how many viewers there are. TW gets permission to copy my stuff in exchange for something valuable – we have a contract.
I have no contract with you. You have a contract with TW. Your contract with TW may allow you to watch the stuff once, or any number of times between certain times. TW cannot grant you the right to watch stuff that some other party also happens to make available (be it legally or illegally). Your right to watch at the scheduled time depends on a chain of rightful permissions, where TW can legally distribute because of their contract with me, and you can legally watch on TW because of your contract with them. The pirate source has no legal right to my stuff, so you cannot gain a legal right to my stuff from them.
Also FYI in the US there is no legal defense "I didn't know that the pirate source was distributing illegally" (known as "innocent infringement").
Does the original copyright (or the fact that it allowed me to watch it), allow me to source the content elsewhere?
No. Because copyright does not allow you to watch anything. Copyright is a prohibition on making unauthorized copies, not a right to do anything.
