Yes, the "bad" events adding up to the interpolated values can be removed or overwritten. Though both are not very common in PI systems.
Maybe you can share a bit more information on the issue you are working on?
Did you want to expand on your question any further so that we could assist you? From what you provided so far, I would say that if you are using PI Web API for data access and are sampling a pi tag every 15 min, the data quality for the tag should be independent of the PI Web API call. Based on the context you have provided thus far, I would say that given the quality of data on the PI Server side, you could expect good values in the future at any of the different given intervals or bad quality data. It all depends on the data being sent to the PI Tag from the data source. Please let me know if this addresses your question or if you feel there is something you could expand on to give us better context into your question.
Hope this helps!