When I was walking versus While I was walking

(Grammar Questions I Couldn't Answer)

A student wrote in her essay "One time,when I was walking in the outside, I met a person."

We were going over this sentence in class.  I had in mind other errors (in the outside), but one student asked about "when".

"Shouldn't it be 'while I was walking' ?" she asked.

My native speaker intuition told me both "when" and "while" were acceptable here, but I couldn't explain why.

So I looked it up in Practical English Usage by Michael Swan.

Swan says (on p.67-68) that there are some differences between when and while.   For example, while can be used for simultaneous events, and when can not.

However, in some cases they are interchangeable.

As Swan says on page 67:

We can use all three words [as, when, while] to introduce a 'backgound' action or situation, which is/was going on when something else happens/ happened

I wonder, though... Even though we can use both when and while in this sentence, is there any change of nuance?