In “Mindfulness Defined” (available free here), Thanissaro Bhikkhu writes:
“The Buddha discovered that the way you attend to things is determined by what you see as important—the questions you bring to the practice, the problems you want the practice to solve. No act of attention is ever bare. If there were no problems in life you could open yourself up choicelessly to whatever came along. But the fact is there is a big problem smack dab in the middle of everything you do: the suffering that comes from acting in ignorance. This is why the Buddha doesn’t tell you to view each moment with a beginner’s eyes. You’ve got to keep the issue of suffering and its end always in mind.”
In Mindfulness in Plain English, Henepola Gunaratana writes:

“Mindfulness is nonconceptual awareness. Another English term for sati is ‘bare attention.’ It is not thinking. It does not get involved with thought or concepts. It does not get hung up on ideas or opinions or memories. It just looks. Mindfulness registers experiences, but it does not compare them. It does not label them or categorize them. It just observes everything as if it was occurring for the first time. It is not analysis that is based on reflection and memory. It is, rather, the direct and immediate experience of whatever is happening, without the medium of thought. It comes before thought in the perceptual process.” (pg 140)
If you read both pieces in their entirety, it is even more apparent how contradictory they are concerning what mindfulness is and isn’t. Thanissaro Bhikkhu even gets a little snippy, writing “popular books on meditation . ..offer a lot of other definitions for mindfulness, a lot of other duties it’s supposed to fulfill—so many that the poor word gets totally stretched out of shape. . . These are not just minor matters for nitpicking scholars to argue over.”
Both authors are Theravadins and both are accomplished monks, although the former is from the Thai forest tradition and the latter is from Sri Lanka. I don’t know very much about Theravada, so I don’t know if their different perspectives stem from divergences in their respective traditions.
In any case, I think it’s a good example of why it’s important for authors to specify what exactly they are basing their assertions on, and also to specify when they are speaking from the perspective of a particular tradition with which other traditions disagree. Buddhism may seem confusing at times, but it would be less confusing if authors did this more often.