Detecting empathy from video interactions has emerging applications, yet raw videos that could be used for training AI models are rarely available due to privacy and ethical constraints. Public benchmarks are consequently released only as pre-extracted features, creating a privacy-constrained learning regime whose privacy-utility trade-off is poorly characterised. We formalise three levels of privacy for video-based behavioural prediction -- no privacy (raw video), partial privacy (temporal visual features such as facial landmarks, action units and eye gaze) and strong privacy (summary statistics of those features) -- and ask whether strong, subject-generalisable empathy detection is achievable at the strong-privacy level. We propose TFMPathy, instantiated with two recent Tabular Foundation Models (TFMs) (TabPFN v2 and TabICL), under both in-context learning and fine-tuning paradigms. On a public human-robot interaction benchmark, TFMPathy achieves strong utility under strong privacy, outperforming established baselines by a substantial margin. To assess robustness and facilitate fair, safe deployment, we introduce a cross-subject evaluation protocol that was previously lacking in this benchmark. Under this protocol, TFM fine-tuning improves generalisation capacity substantially (accuracy: $0.590 \rightarrow 0.730$; AUC: $0.564 \rightarrow 0.669$). Aggregating temporal features into summary statistics also suppresses subject-specific and demographic cues, aligning TFMPathy with data-minimisation principles. TFMPathy, therefore, offers a practical route to building AI systems that depend on human-centred video when governance, consent or institutional policies restrict the sharing of raw video. Code will be released upon acceptance at https://github.com/hasan-rakibul/TFMPathy.