Generating stylized large language model (LLM) responses via representation editing is a promising way for fine-grained output control. However, there exists an inherent trade-off: imposing a distinctive style often degrades truthfulness. Existing representation editing methods, by naively injecting style signals, overlook this collateral impact and frequently contaminate the model's core truthfulness representations, resulting in reduced answer correctness. We term this phenomenon stylization-induced truthfulness collapse. We attribute this issue to latent coupling between style and truth directions in certain key attention heads, and propose StyliTruth, a mechanism that preserves stylization while keeping truthfulness intact. StyliTruth separates the style-relevant and truth-relevant subspaces in the model's representation space via an orthogonal deflation process. This decomposition enables independent control of style and truth in their own subspaces, minimizing interference. By designing adaptive, token-level steering vectors within each subspace, we dynamically and precisely control the generation process to maintain both stylistic fidelity and truthfulness. We validate our method on multiple styles and languages. Extensive experiments and analyses show that StyliTruth significantly reduces stylization-induced truthfulness collapse and outperforms existing inference-time intervention methods in balancing style adherence with truthfulness.