The odd thing is, comma placement [duplicate]

“The odd thing is, she has no idea who he is and why she got all of his heritage.”

I would normally identify this first sentence as having a nominal that-clause acting as a subject complement with the “that” omitted. Which is fine, but it would mean it's incorrect to use a comma in that position, but I get the hunch, the inkling that it is correct even while the sentence below cannot take a comma no matter what. Am I just plain wrong? Would there be any other real grammatical reason for there to be a difference other than emphasis?

“The odd thing is that she has no idea who he is and why she got all of his heritage.”

Solution 1:

With the comma, the speaker is making a comment about the statement she has no idea... This is similar to using "hopefully" as a sentence adverb as in Hopefully, he'll come early. Without the comma we have Odd thing = She has no idea that ..., which is more of a statement equating something to being odd. I see a difference in emphasis: I find it odd that... or *Isn't it odd that...?" versus It's odd that... With the comma I feel the presence of a speaker; without, it has a more narrative feel.

There is an analogy with cleft sentences, which emphasize a later part of a standard-order sentence by bringing it forward (You ate my cookies! -> Those were my cookies you ate!), except here the emphasis is achieved by "detaching" the odd, which is already at the beginning. Perhaps pointing out the oddness was a recent decision.