I believe this would be more of an issue with disputes about domain ownership than with company information. It does make you look less reputable since you are trying to hide your business contacts and information, but I can't see how this would let somebody make a complaint about your website.
It could affect the ownership of your domains, though. There are ways that such services could still assign you as the actual owner, but the way that some companies work, the domain name technically would not belong to you per ICANN rules, meaning that you would have a harder time disputing it if the need ever came up. Even if they do play by the rules, having the WHOIS information obfuscated could at the very least cause you a hassle if you ever try to transfer your domain. The registrars would be sending the verification email to the address on the WHOIS record, which you would not likely be able to access directly. Fortunately, in most cases, these situations aren't too much of a problem.