Social robots have emerged as valuable contributors to individuals' well-being coaching. Notably, their integration into long-term human coaching trials shows particular promise, emphasizing a complementary role alongside human coaches rather than outright replacement. In this context, robots serve as supportive entities during coaching sessions, offering insights based on their knowledge about users' well-being and activity. Traditionally, such insights have been gathered through methods like written self-reports or wearable data visualizations. However, the disclosure of people's information by a robot raises concerns regarding privacy, appropriateness, and trust. To address this, we conducted an initial study with [n = 22] participants to quantify their perceptions of privacy regarding disclosures made by a robot coaching assistant. The study was conducted online, presenting participants with six prerecorded scenarios illustrating various types of information disclosure and the robot's role, ranging from active on-demand to proactive communication conditions.