I have read the Spencer and Braswell paper you just linked to.
There are some difficulties.

First, it is a modelling paper - it uses a climate model developed by Spencer himself, but it is too simplistic to really approximate Earth's complicated atmosphere-ocean feedbacks. In fact, the water cycle and El Nino/Southern Oscillation (ENSO) are not included in the model.

Second, this model assumes that El Nino/Southern Oscillation is driven by changes in cloud cover (as opposed to many scientists who have presented evidence that ENSO drives changes in cloud cover (i.e. Spencer may have his cause and effect reversed). So this is some justification (possibly incorrect) for neglecting ENSO, but it is still neglected in the model.

Third, their model was developed using only a single data set - a good model needs to be built or trained on one data set, and then fed completely different ones. This is a very basic principle of any type of modelling.

Fourth, details regarding their modelling algorithms and assumptions have not been released, so the results cannot be independently confirmed (remember Pons and Fleishman?).

So, while the paper you provided can certainly not be called "wrong", it is currently *unsupported*.
So, in this case, I agree with you - certainly not a useful model (at this point).

A colleagues says all the time "all models are bad, but some are useful".