I don't get why you need science for this, it's a linguistic thing. It's just the name for a particular situation, not a statement that certain things can be predicted from other things.

1. Thing happens that isn't widely reported.
2. The person responsible fears word getting out and chooses to make attempts at suppressing awareness of the Thing.
3. Suppression attempts get reported on, and news about the whole situation - original Thing and also Suppression - get more widely reported on.

This whole thing is a chain of events that could happen, and, if it does, then this is called the Streisand Effect.

If any part of it doesn't happen - if the person doesn't fear the situation, or if they doesn't make suppression attempts, or if the the suppression attempts actually work and the story dies, or if the suppression attempts don't work but still no one much cares - then it's just not the Streisand Effect.

Terming it an "effect" does seem to imply that it's stating a meaningful prediction, that there is a serious liklihood of things progressing this way based on initial choices.

Think of it as kind of like the weather. There are multiple competing and cooperating underlying factors that combine to some actual weather result. One of those effects, left to its own devices, causes rain, but the existence of that effect doesn't mean every scenario involving that factor will lead to rain, since other things could interfere.

Reddit page where people discuss this exact conversation.

Edit: I realize I basically start by saying the Streisand Effect shouldn't primarily be thought of as a causative thing, and then later compare it to factors that affect the weather, themselves causative things.

The Streisand Effect is, basically: what happens when you try to suppress something, should news of that suppression lead to drawing much greater attention to the original thing than would otherwise have occured. "Congratulations, you played yourself." It's not prescriptive - attempts to suppress don't inherently lead to the blowup. You could also think of it as the "Overcompensation Effect", what happens when attempts at correction cause a new problem - though the Streisand Effect is very specifically not about the news of the cover up as an end, but as a means to the original story news blowing up.