Hello Nimbleswitch.
The accidentals on a chart (for certain songs) are for reference. Often I find they're plain wrong, or for "comfort" purposes (as in, simply a reference for referring to a song's key when talking about it, or calling it in a gig).
The *real* indication of a song's key is that song's harmonic progression itself, or - as in "SW"'s case, which has no real progression - its tonal center.
"SW" is "in" Dm, since that is the main chord throughout (whatever mode that would/could be), and our brain feels that as a resting point. That is what we mean/indicate by saying a song is *in* a certain key.
The B-section is a tension-creating episode, perceived as such by our brain because A) the primary acoustical reference is both the (starting and persistent) Dm chord, and the bass line defining the note D as a central rest-point, and B) the chord a half-step above Dm creates tension because when we return to Dm we feel rest - so we call D the tonal center, or Tonic.
Our ears tell us this *before* the chart's existence, which is just convenience.
Ergo, a "SW" chart with no key signature is not indicating the song is in C, or Am - it "indicates" nothing in regard to key; it's an absent sign, not a sign (even though dflat's reasoning is also valid).
Further, I would regard a Bb in key as valid in indicating Dm, but obviously I'd see - by reading the bass line - that a Dm dorian would be more appropriate to improvise with than a Dm natural (but of course I'm free to do many other things as a soloist, in my creative freedom... ;-) )
Saying "SW" is in Am would indicate the note A is its tonal center - but nothing in the original song recording (or the music written in common charts) pushes my ears and eyes in perceiving A as an important note...
That is why I say "it's in Dm", and set it as such in the iReal Pro chart info. Otherwise, if one were to say "play SW in Am", I'd play "A-E-F#-G-A-B-G-A" (note A as tonal center).
I hope the reasoning is clear. I posted here instead of PMing you, though lengthy, because perhaps others can benefit from the analysis
P.S.: short, incomplete answer

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you say
Just because the Dm chord dominates, does not make it written in the key of D minor
, but that is *exactly* why our perception makes us say the song is in Dm...