Please read the following background paragraph carefully to understand the meaning of "review" in this question - it may not be what you think. In particular, this is not a duplicate of Is it acceptable as referee to contact an author on a paper you review?, and the peer-review and review-articles tags are not really applicable here.
In mathematics, we have two well-known "review databases": MathSciNet / Mathematical Reviews and Zentralblatt MATH (aka zbMATH). These services aim to create a comprehensive database of papers that have already been published in peer-reviewed journals. For each recently published paper, they invite an independent expert in the subject (not one of the authors) to write what is (perhaps confusingly) called a "review", which is really just a synopsis of the paper's content - a sort of third-party extended abstract, perhaps 1-4 paragraphs long. The review is generally not expected to make a judgment of the paper's quality or novelty, though it may cite other papers for context. When the review is finished, it is posted in the database along with bibliographic information for the paper, including the reviewer's name (so these reviews are not anonymous). The databases are available by subscription, and are the field's primary tool for literature searches.
I have been invited to review a paper for zbMATH. In reading the paper, I got confused by some notation that seems to be unclear; it could be an error or omission in the original paper, or maybe just something I have overlooked. I would like to contact the authors to ask for clarification. Is it appropriate for me to contact them directly? If so, should I identify myself as a zbMATH reviewer, or just a reader with a question?
I can't think of any concrete reason not to do so. My review will eventually be printed with my name, so I don't have anonymity to protect, and it won't say anything controversial. But I do have some vague sense that my review is supposed to be "independent", so I am hesitating.
I suppose I can ask the zbMATH editors / administrators, but I would also be interested in opinions from the community.
(Note that the database editors are not generally in contact with the authors of the paper - they just grab the published papers and send them out to reviewers. So it isn't as though I would use the editors as an intermediary.)
For reference, the invitation from zbMATH reads as follows:
[W]e would like you to contribute a review of the attached item for zbMATH. We hope that you will find the publication to be of interest to you. We would appreciate if your review would give an independent description. If you cite parts of the original text please label extensive verbatim quotations as such.
More information about what is expected in a review can be found at https://zbmath.org/reviewer-service/, but the issue at hand is not addressed.