Grammar and usage

"Not without" is a double negative that means "with".

Thus, your sentence becomes "With reason, some scholars think it doubtful."

We often hear that using a double negative is "poor grammar."  This advice comes when someone is generally using poor grammar all around. "I don't got no apples"  actually means "I have apples" but the speaker is using poor grammar with the intent to say he has no apples.  The Rolling Stones "can't get no satisfaction" and this technically means the opposite of the intended message.  They have taken poetic license with grammar.

A double negative, when properly used, is indeed correct grammar.  It is used when the positive is not quite the whole picture or completely accurate.  In your example, the scholars do have a reason to be doubtful.  The double negative implies that they probably have reason to think otherwise, though.

If I am lost in the wilderness and on the brink of starvation, I will try to eat something distasteful or potentially poisonous.  I don't want to not eat.  The double negative here means that I do want to eat, but I would prefer that I didn't have to.

He isn't ugly.

She is not unfamiliar to me.

I can't not be nervous before the big event.

With some justification, scholars believe...