Under what circumstances can the word "be" be used directly without any change? [duplicate]
To summarize the results in the comments:
Sentence 1 exhibits an improper use of the subjunctive be in a clause complementing announced. It should be replaced with an ordinary indicative.
Sentence 2 exhibits an ordinary use of the mandative subjunctive, which is experiencing a comeback in BE, possibly under the influence of AE formal use. It is often replaced with a construction using should.
The quotation from Sidney exhibits a different, non-subjunctive use of be; it is obsolete and not productive in contemporary written or spoken English.