As a VWP traveler who is generally entering the US in transit to another country, I'm rather absent-minded at immigration, usually sleepy and jetlagged, just going through the motions.
You don't have to give a lot of thought to what you're saying, because you just have to answer each question truthfully and move on.
Once, I was asked by the immigration officer if I had anything in my backpack that was bought in the origin country (where my flight had departed).
I didn't remember. I knew exactly what I had in my backpack, which were a lot of personal computer accessories, but I certainly don't keep track of, say, where I bought a USB stick.
So of course that's what I said - "I don't remember".
That has been the only weird experience at US immigration that I've ever had. The officer instantly changed his demeanor, and turned increasingly hostile (while still professional), asking the same question multiple times, telling me that he was in no rush and he could keep me at the airport all day if needed.
That woke me up. Sleepiness was gone, and as you say, I was afraid that I would have to go through unnecessary complications. But here's the thing: I was telling the truth, so I just kept on politely repeating the same answer.
After four or five times, as I didn't want to sound defiant by simply repeating the same answer again and again, I added something like "Officer, I'm sorry, I really don't remember. Perhaps we can move to a room, open my backpack, verify the contents and you can let me figure out what was bought where."
He smiled, stamped my passport and he welcomed me to the United States.
This doesn't seem an answer to your question, but it is:
So can I choose 'No' to avoid unnecessary complications?
You can't choose what to say in order to manipulate the outcome of the interview. You have to answer any question truthfully.
When in doubt, be open! Provide all the information you have.
It will be up to immigration to decide if it's relevant or not.
I told you about my episode because it shows that telling the truth, even when the answer isn't great, or it isn't what you think they want to hear, doesn't necessarily lead to unnecessary complications.
Conversely, as described or implied by all other answers, lying can and most likely will lead to unnecessary complications.
Do not lie to immigration, ever.
Well unless you're looking to be banned, of course.
Another example: you're entering a country that is asking you if you're carrying food, but you're not sure if what you're carrying is classified as food? Just say YES. Let the interviewer ask you and find out if what you have is acceptable.
It's better to look stupid or naive or excessively compliant, rather than raise suspicions by hiding something that you think didn't matter. Let them decide.