It is most probably a simple double-check in order to confirm you're the actual person that the passport represents. Most probably this is prompted by your recent looks being very different from your picture in your passport.
Yes a passport (with a valid authorization) is sufficient to consider your application for entry, but before that the officer needs to be satisfied that the passport does actually represent you.
Whether you should provide another ID or not is subjective, you decide. For me, I don’t play right or wrong with immigration officers. If they ask for something and I have an answer, I do provide it regardless of whether I should have had to or not.
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Anecdote
When I posted this answer, the OP didn't really seem to believe that this answer was right. As fate would have it I was naive enough to fall victim to this scenario and guess where? Russia!.
My passport has a 3 year old photo of mine without any beard (with mustache) and for the World Cup I'm sporting thick beard which took months to grow. My FAN ID has my picture with the beard. I don't know why it never occurred to me that the mismatch with passport could be a problem, I was going to Russia and I should have known better about Russian Immigration staff.
As soon as it was my turn and I handed over my passport, the Immigration officer started alternating his gaze between my face and my passport. Those were the longest 2 minutes of my life. After he was done trying to match my face with the picture he started scanning my passport to check if it was fake. He checked the bio page under a magnifier with some special light, then checked the stitching on the passport over and over. Then he did the same to the very own FAN ID that Russia issued to me.
After he was done with the verification of documents he asked me:
Do you have a ticket for the match?
Yes, here it is
Do you have a return ticket out of Russia?
Yes, here it is
Do you have any friends with you today?
No
Do you have hotel booking?
Yes, here it is
Do you have any other ID with you?
Yes, here are my 2 previous passports and my driving license.
At that point he started to return the documents one by one to me and at the end stamped me in and said Welcome to Russia, Have a good night.
Guess what? The immigration officer on exit repeated the same process to verify if my passport and FAN ID actually belonged to me. It was my first time in Russia and I Love it, but Russian Immigration is the last authority you want to take such fashion chances with.
Things better match up!
Note: In all fairness to them it was my own fault, and they were just doing their job and at no point I was put under undue stress or taken somewhere other than the counter I reported to and apart from the longest 10 minutes ever, everything went well.