Taking into account reliability of Raven's Matrices and Self Monitoring tests
Regarding Cronbach's $\alpha$, Wikipedia writes:


  It has been proposed that $\alpha$ can be viewed as the expected correlation of two tests that measure the same construct.


Note that correlation is a nonparametric concept. Its definition is independent on the functional form and functional relationship of the two variables. There are numerous ways to measure correlation that take the functional form into account. Pearson correlation and point-biserial correlation are probably the most well known.

In the case of two binary variables some notable measures are: Matthews correlation coefficient, Cohen's $\kappa$ or Pearson's $\phi$. One may also consider measures from Signal detection theory. Cronbach's $\alpha$ is also applicable to binary variables. In fact, the Wikipedia page lists a simplified formula (due to Cronbach, 1970) for the case where both variables are binary.

To conclude, there is nothing wrong with application of Cronbach's $\alpha$ to binary items. Still, other measures of relationship between two binary variables exist and may be worth considering.  

Reference: Cronbach LJ (1970). Essentials of Psychological Testing. Harper &amp; Row. p. 161.