In e-commerce service recommendation, utilizing auxiliary behaviors to alleviate data sparsity often relies on the flawed assumption that auxiliary behaviors that fail to trigger target actions are negative samples. This approach is fundamentally flawed as it ignores false negatives where users actually harbor latent intent or interest but have not yet converted due to external factors. Consequently, existing methods suffer from sample selection bias and a severe distribution shift between the auxiliary and target behaviors, leading to the erroneous suppression of potential user needs. To address these challenges, we propose a Noise-to-Value Adapter (NoVa), an e-commerce service recommendation framework that re-examines the problem through the lens of positive-unlabeled learning. Instead of treating ambiguous auxiliary behaviors as definite negatives, NoVa aims to uncover high-quality preferences from noise via two key mechanisms. First, to bridge the distribution gap, we employ adversarial feature alignment. This module aligns the auxiliary behavior distribution with the target space to identify high-confidence false negatives, which are instances that statistically resemble confirmed target behaviors and thus represent latent conversion intents. Second, to mitigate label noise caused by accidental clicks or random browsing, we introduce a semantic consistency constraint. This mechanism implements semantic-aware filtering based on the content similarity of services, acting as a bias correction step to filter out low-confidence interactions that lack semantic relevance to historical user preferences. Extensive experiments on three real-world datasets demonstrate that NoVa outperforms state-of-the-art baselines.