Accurate placement of the nasogastric (NG) tube is essential for patient safety. However, manual radiographic interpretation is time-consuming and prone to error. Existing deep learning methods, while promising, often separate classification and segmentation and lack mechanisms to address data imbalance or prediction reliability. To overcome these limitations, we propose an AI-assisted NG tube placement assessment system incorporating three key innovations: (1) a Joint Model that concurrently performs classification and segmentation by extending nnU-Net with an additional classification branch; (2) a Class-Balanced Loss that combines deferred re-weighting and reverse KL divergence to mitigate class imbalance; and (3) a Reliability Filtering module that eliminates uncertain predictions using classification uncertainty, twist detection, and a consistency check based on Pearson correlation. To evaluate the effectiveness of our system, we conducted extensive experiments using multi-institutional datasets, the external MIMIC-CXR dataset, and data from an independent hospital. The results demonstrate the robustness and generalizability of our integrated approach. Specifically, the Class-Balanced Loss improves sensitivity and balanced accuracy, while the Reliability Filtering module enhances the trustworthiness of predictions. These findings underscore the potential of our method to support safer and more efficient clinical decision-making in NG tube placement assessment.