[Grammar] confused with grammar - The doctor recommended he gives up smoking

[HeartShape]

The subjunctive is discussed in Huddleston and Pullum (2002), The Cambridge Grammar of the English Language: especially pages 993-1001.

According to Huddleston and Pullum (2002), The Cambridge Grammar of the English Language: especially pages 993-1001.

1. It's vital that they be kept informed. [subjunctive]
2. It's vital that they are kept informed. [non-subjunctive]

From BBC Roger's teaching material, sentence 2 below contains (technically) a non-subjunctive clause. Is this correct?

1. The government tried to insist (that) all firearms should be handed in without delay.
2. The government tried to insist (that) all firearms are handed in without delay. [non-subjunctive]