It's similar in English. In conversational German we aren't exactly as concerned about perfect grammar as we are in getting the message across. "I went to the store yesterday...Walgreens that is; not Walmart..." Not a pretty sentence, but we add this to include information conversationally. We usually don't go back to correct the first sentence: I went to Walgreens yesterday...
Sometimes we simply add a short phrase like "das heißt" or "ich meine" or "besser gesagt" to introduce the additional information in German.
