Both examples are technically grammatical:
- A little is known about the author of this book.
- Little is known about the author of this book.
However, the second sentence is much more idiomatic and likely to be said. Little is known about X is a common way to phrase things, but the version with a little is not commonly said, so it's not really surprising that people would consider it a mistake.
People tend to expect things to fit the patterns they're used to hearing, and if you say something that almost fits a pattern they know, they're likely to think you made a mistake. If they heard sentence 1, they'd probably think you meant to say sentence 2, even if both versions are technically grammatical.
Both a little and little are quantifiers which express small numbers. So what's the difference?
- A little is a positive paucal1 quantifier, indicating that a small amount does exist. The emphasis is on the existence of a quantity, even if it's small.
- Little is an approximate negative quantifier, expressing that an amount is almost but usually not quite zero. The emphasis is on the lack of existence, even though a very small amount may exist.
As a negator, little licenses negative polarity items:
Very little is known at all about the author of this book.
This would be ungrammatical with a little, which is positive:
*A very little is known at all about the author of this book. ← ungrammatical
The same is true of a few (positive paucal quantifier) and few (approximate negative quantifier).
1 From Latin paucus 'few; little', indicating a relatively small number.