I don't quite understand this one.
When you have a saved visualization that you share via a link, it is already tied to an index pattern. In fact, once you create a visualization, the index pattern it's tied to is fixed and cannot be changed without messing with advanced options in Settings.
This is unlike the question about the time range in the other thread. Once you share visualization through a link with someone, when they click on it, they are taken to the Kibana UI. Once there, they can adjust the date pretty easily. I commented with some details on future enhancements and suggested workarounds on that thread.