A researcher may decide that a taxon is actually polyphyletic if

If the two organisms descended from different ancestors

Explanation:

In taxonomy, organisms are placed into different groups called taxon. This is usually on the basis of their shared characteristics.

Based on characteristics, polyphyletic taxon can be formed.

Polyphyletic means unrelated organisms from different recent ancestor.

However, a researcher may decide that a taxon is actually polyphyletic if the organisms in the organisms placed in that group do not share a common ancestor.