Users report that they have regretted accidentally sharing personal information on social media. There have been proposals to help protect the privacy of these users, by providing tools which analyze text or images and detect personal information or privacy disclosure with the objective to alert the user of a privacy risk and transform the content. However, these proposals rely on having access to users' data and users have reported that they have privacy concerns about the tools themselves. In this study, we investigate whether these privacy concerns are unique to privacy tools or whether they are comparable to privacy concerns about non-privacy tools that also process personal information. We conduct a user experiment to compare the level of privacy concern towards privacy tools and non-privacy tools for text and image content, qualitatively analyze the reason for those privacy concerns, and evaluate which assurances are perceived to reduce that concern. The results show privacy tools are at a disadvantage: participants have a higher level of privacy concern about being surveilled by the privacy tools, and the same level concern about intrusion and secondary use of their personal information compared to non-privacy tools. In addition, the reasons for these concerns and assurances that are perceived to reduce privacy concern are also similar. We discuss what these results mean for the development of privacy tools that process user content.