When analyzing organic search there is the possibility to use 'search engine natural'.
This dimension does not apply the processing rules like marketing channel, and thus is expected to give a more clean view of the actual performance of organic search.
However, when I use this dimension in combination with entries, and I put 'Paid search' (dimension) below it, I still get data.
When I use this dimension in combination with visits, this does not seem to be the case.
Can someone explain why we see 'paid' when we use the 'entries' metric? (see snippit)
The first thing I would recommend doing is building a venn diagram with 'visit: Paid Search - Paid' as one segment, 'visit: paid search - Natural' as another and visits at the metric. This will show you the frequency at which you have visits from both referrer types.
Beyond that the entries and exits metrics are not only related with the hit at which it occurred. So its plausible that your segment is returning hits where the referrer was natural search, but within the same visit the entry on the page occurred from a different referrer.
You can validate this theory by adding a hit depth = 1 to your segment. This will likely remove any paid search instances for your entries column.