You don't understand what pigeonholing really means.
When programmers talk about pigeonholing it usually means they like Python and want to go at Python conferences where people talk about math, science and machine learning, but they are pigeonholed in Java EE and surrounded by people who only talk about POJOs and beans.
And to top it all off, Java experience is badly regarded in Python tech companies and long term pigeonholing usually cuts you off from the world you want to be in.
I second sdeveloper's comment. This is about establishing authority, not being pigeonholed. Pigeonholing is something done to you regardless of what you do. Pigeonholing doesn't make you the #1 result on Google for a term. Pigeonholing tells you that because you're the #1 result for "French chef" in Google, you're not qualified to make tacos.
You're right, that part of the interview really was more about the fear of pigeonholing for the independent dev/consultant, not the actual results of pigeonholing for the FTE.
When programmers talk about pigeonholing it usually means they like Python and want to go at Python conferences where people talk about math, science and machine learning, but they are pigeonholed in Java EE and surrounded by people who only talk about POJOs and beans.
And to top it all off, Java experience is badly regarded in Python tech companies and long term pigeonholing usually cuts you off from the world you want to be in.