It's not impossible.
I have worked on research involving a child born as illegitimate in Scotland in 1880. Her mum married three years later to man she and her child had been staying with in 1881. Child brought up with her mum, step dad and their subsequent children. Step dad's surname generally used in Census returns, but her birth surname (ie her mum's maiden name), used on child's marriage record and no dad listed. Her death was indexed under her married and birth surnames, again no dad listed and her mum noted as 'afterwards married to'.
Fast forward to DNA, and from viewing matches of various descendants of the child, it soon became obvious beyond very little doubt, that either her step-dad or one of his male siblings, was most likely her actual dad.
Something to consider, despite b/m/ds suggesting to the contrary.
That said, in your case, being 'comfortably accepting' is a choice only you know if you will be happy with, or if it will still leave you with niggling doubts. It is a choice that will not alter the fact, whatever that fact actually was (ie father/not father). If you want more certainty, then DNA might give this.