It's said that the grammar structure had to have done can be used instead of must have done when drawing a conclusion about a past event. For example:
You said somebody played the piano 6 pm yesterday. It had to have been Kate. She always does.
But, I've heard people say it had to be instead of it had to have been, it seems, in the same way. For example:
You said somebody played the piano 6 pm yesterday. It had to be Kate. She always does.
Is there any difference in meaning between it had to be and it had to have been when drawing conclusions about past events?