Considerable effort has been made in privacy-preserving video human activity recognition (HAR). Two primary approaches to ensure privacy preservation in Video HAR are differential privacy (DP) and visual privacy. Techniques enforcing DP during training provide strong theoretical privacy guarantees but offer limited capabilities for visual privacy assessment. Conversely methods, such as low-resolution transformations, data obfuscation and adversarial networks, emphasize visual privacy but lack clear theoretical privacy assurances. In this work, we focus on two main objectives: (1) leveraging DP properties to develop a model-free approach for visual privacy in videos and (2) evaluating our proposed technique using both differential privacy and visual privacy assessments on HAR tasks. To achieve goal (1), we introduce Video-DPRP: a Video-sample-wise Differentially Private Random Projection framework for privacy-preserved video reconstruction for HAR. By using random projections, noise matrices and right singular vectors derived from the singular value decomposition of videos, Video-DPRP reconstructs DP videos using privacy parameters ($\epsilon,\delta$) while enabling visual privacy assessment. For goal (2), using UCF101 and HMDB51 datasets, we compare Video-DPRP's performance on activity recognition with traditional DP methods, and state-of-the-art (SOTA) visual privacy-preserving techniques. Additionally, we assess its effectiveness in preserving privacy-related attributes such as facial features, gender, and skin color, using the PA-HMDB and VISPR datasets. Video-DPRP combines privacy-preservation from both a DP and visual privacy perspective unlike SOTA methods that typically address only one of these aspects.