Mixing present and past tense in a report or public announcement

1) In the subordinate clause of the following sentence, what is the proper verb tense of to be?

She made a statement that Michael is/was a suspect.

(When, in reality, Michael is not a suspect)

2) Will it be the same if the verb in main clause is in negative?

She never made a statement that Michael is/was a suspect.

Answer

Both are correct and whether you use the former or the latter depends solely on whether the implications of the statement are still valid today or were valid only in the past. With that said, consider the following:

Jane tried to explain that John was really sick. It's a shame nobody believed her. Now that he's dead, it doesn't even matter anymore.

versus

Jane tried to explain that John is really sick. I think we should visit him and find out for ourselves; what if he needs medical attention?

The same rule applies to negatives.