In the following situation, do you believe and/or trust your SO?

Say, you and your SO are out in the city center, enjoying a day off, do some shopping and eat and drink something.
Then, a stranger (to you) approaches the both of you and starts talking to your SO, calling her by a different name .
Your SO is denying and ignoring the stranger, but you think you can tell that SO is uncomfortable.
Later, when you are together alone again, you ask your SO what that was all about.
Your SO first answers that it is nothing, but after some persisting tells you that there is ‘something’ but that it is not important and that ‘it’ will not influence your relationship.
“Trust me”, your SO tells you.

So, how would you fare from that point on?
Trust your SO (and trusting that there will be no influencing because/through ‘it’)?
Let it rest?

This was a scene from the police series Wallander that I saw last weekend.
It is not a personal question in that it comes from my relationship.

I, for one, would let it rest (maybe after more confirmation that all is okay) but I would also urge my SO to tell me in due time. at least, that is how I would like to react to it.