I'm not good with my grammatical definitions but I believe this is an example of reported speech. Maybe someone else can correct me. The validity of the 'be' in this case follows from the idea that the facility is not yet built and will be built in the future, also that its intransitive and the subject doing the building is not known, and from the 'that', which is necessary to report for a noun such as 'idea'.
Other examples:
I'm displeased with the notion that this man be promoted before me.
He's supportive of the idea that Taps be played on November 11th.
This is one of those situations where, if the phrase is dwelt on and thought about too much, even by a native speaker, it starts to sound odd, but in actual fact its quite common. If you added 'will' to the above examples the meaning stays the same but the grammar becomes more agreeable.
eg:
I'm displeased with the notion that this man will be promoted before me.
He's supportive of the idea that Taps will be played on November 11th.
I'm against the idea that more nuclear facilities will be built.