
Is the Present Indefinite really OK here? Japanese seems to have a past tense.

It's technically possible, but overly confusing without context.
Take this example.
Fred: What's up with James? He's in a terrible mood today.
Geoff: He had a fight with his girlfriend; I forget the details, but that's probably it.
Geoff forgets (or realises that he has forgotten) the details as he is speaking. I don't think the Japanese has an exact equivalent for that situation, so they'd probably go with the past tense.

Thank you for the explanation.