Using Theils' Mixed Estimation (Dummy observations) to handle zero counts

Consider a binary response $$Y$$ and two binary predictors $$X_1$$ and $$X_2$$. Here is some synthetic data to illustrate the problem.

 |            |  Y=1  |  Y=0  |
| X1=1, X2=0 |   50  |  0    |
| X1=0, X2=1 |   3   |  9    |
| X1=1, X2=1 |   16  |  0    |


I would like to fit a logistic regression model of the form $$E(Y) = \beta_0 + \beta_1 X_1 + \beta_2 X_2,$$ but the zeros in the table above make this an ill-posed problem. One simple option is to add 1 dummy observation to each cell in the above table, leading to

 |            |  Y=1  |  Y=0  |
| X1=1, X2=0 |   51  |  1    |
| X1=0, X2=1 |   4   |  10   |
| X1=1, X2=1 |   17  |  1    |


This makes it possible to fit the logistic regression model. This approach seems similar to Theils' Mixed Estimation method in econometrics, and clearly has a Bayesian flavor (and interpretation).

Some general questions are

1. Is this solution for handling the zero-counts justifiable?
2. Is there a clear Bayesian interpretation for this, like in Theils method for regression?
3. Is there any literature which does something similar?
4. Is there a better way to approach this?