How does the Y combinator exemplify “Lambda calculus inconsistency”?

Question

On the Wikipedia page for Fixed Point Combinators is written the rather mysterious text

The Y combinator is an example of what makes the Lambda calculus inconsistent. So it should be regarded with suspicion. However it is safe to consider the Y combinator when defined in mathematic logic only.

Have I entered into some sort of spy novel? What in the world is meant by the statements that $\lambda$-calculus is "inconsistent" and that it should be "regarded with suspicion"?