Irrespective of the success of the deep learning-based mixed-domain transfer learning approach for solving various Natural Language Processing tasks, it does not lend a generalizable solution for detecting misinformation from COVID-19 social media data. Due to the inherent complexity of this type of data, caused by its dynamic (context evolves rapidly), nuanced (misinformation types are often ambiguous), and diverse (skewed, fine-grained, and overlapping categories) nature, it is imperative for an effective model to capture both the local and global context of the target domain. By conducting a systematic investigation, we show that: (i) the deep Transformer-based pre-trained models, utilized via the mixed-domain transfer learning, are only good at capturing the local context, thus exhibits poor generalization, and (ii) a combination of shallow network-based domain-specific models and convolutional neural networks can efficiently extract local as well as global context directly from the target data in a hierarchical fashion, enabling it to offer a more generalizable solution.