Why and how commonly are scientists concerned about open peer review? Some years ago I published an article in a Copernicus Open Access Journal. They have a peer review process called Interactive Public Peer Review, i.e. the pre-print and the reviews are open access. Additionally, everyone can submit a comment on the pre-print. 

I liked this openness, although I didn't get any extra comments other than those of the reviewers.

Some days ago another scientist told me that several scientists have concerns about this openess. They don't like the idea that their work can be commented by everyone. 

I would like to know why there are concerns and how many scientists have concerns about this sort of peer review process.

Are there any studies or surveys answering this question? Are there any reports about the effects of this sort of peer review process?
This answer discusses a survey that indicates blind reviews are much preferred to open ones.  The main reason, from that answer, seems to be


Many people don't want to review non-anonymously.  I know many people on both sides of the fence on this issue.  Once concern is that authors are often sensitive to criticism and may harbor ill-feelings against a person who gives an unfavorable review (especially if the reviewers have not properly understood the paper).  Consequently, open reviewers may be biased (more so than blind reviewers) to colleagues they respect or want a good relationship with.  


Fomite mentions a couple of other issues, but I see this as the main one (and it seems the survey does too).  Some other potential issues are


Certain "rivals" or "critics" can try to ruin your career by giving unfairly harsh reviews.
Some well-respect person could make a comment based on a cursory read of the paper that ends up heavily influencing the reviews, and maybe no one reads the paper carefully enough.