Why training a Restricted Boltzmann Machine corresponds to having a good reconstruction of training data?

Question

Many tutorials suggest that after training a RBM, one can have a good reconstruction of training data just like an autoencoder.

An example tutorial: https://deeplearning4j.org/restrictedboltzmannmachine

But the training process of RBM is essentially to maximize the likelihood of the training data. We usually use some technique like CD-K or PCD, so it seems that we can only say that a trained RBM has high probability to generate data which is like training data (digits if we use MNIST), but not correspond to reconstruction. Or are these two things just equivalent in some way?

Hinton said that it is not a good idea to use reconstruction error for monitoring the progress of training, this is why I have this question.