There is no difference in the first pair. While I agree that #1 is a bit uncommon, most native speaker utterances are based on feelings, not grammar: for that speaker, the loss remains 'his' fault. The same logic applies to your other sentences: the speaker is either thinking about the past or steeped in the present.
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Lissle1.He played very well, and it "is" not his fault we lost.It's not his fault. - A present time judgement on what happened in the past.
Lissle2.Marie failed the exam, but it "was" her own fault - she didn't do any work.It was her fault. - A judgement made about a past time event.
LissleHe played very well, and it is not his fault we lost.Sometimes the use of the present instead of the past extracts the proposition out of historical time and looks at it purely in terms of abstract logic.
Marie failed the exam, but it was her own fault - she didn't do any work.