It really depends on the task. Your model may just be at the point where it’s already able to do the task without adjusting much weights (hence the frozen components don’t matter). It can also be that the unfrozen components can each still adapt on their own and do just fine. It’s hard to say without knowing the transfer learning task and taking a deep look at how the model is training.
I would agree that your second option is the most traditional way of performing transfer learning. I don’t think the first option is all that bad, but if you have confidence that the features learned by the model is sufficient, then it makes sense to just freeze those layers (and probably gain a training speed-up).