Backwards compatibility with pertained model

I am a scientist running some pre-written python scripts/pre-trained models, and I’ve noticed that the scripts will only run properly when the version of tensorflow specified in the script authors’ GitHub readme matches perfectly.
This seems odd to me based on what I have read about tensorflow backwards compatibility in general.
Is this different because it is a pre-trained model? Is this normal? And is there a way to get it to run in newer tf versions?

Backward compatibility to support loading graphs and checkpoints created with older versions of TensorFlow. SavedModel is the preferred serialization format to use in TensorFlow programs. Tensorflow users create SavedModels and load and execute them with a later release of TensorFlow.

SavedModels written with one version of TensorFlow can be loaded and evaluated with a later version of TensorFlow with the same major release. For more details refer to TensorFlow version compatibility.

Please refer to migrate guide to convert TensorFlow code from TensorFlow 1.x to TensorFlow 2 may help you. Thank you