Rocket, in your coin toss example, the problem is that the sample size isn't big enough for the probabilities to play out.
Don't the Climate Change advocates do the same thing when they talk about "record temperatures" as though it's something significant when they've only been keeping records for a 100 years, and the planet is two billion years old?
Exactly, the coin toss where you get 10 heads in a row doesn't disprove that the average toss will be about 50/50. It just proves that interesting things can and will happen.
I believe they mostly talk about record averages and generally across the earth over time - but that is moot. It can definitely be attributed to variance, too. It can always be attributed to variance by someone looking to discredit.
And attributing it to variance is a valid point - as opposed to finding out it is going to be cold tomorrow

The general argument is something like this:
The earth has been getting hotter (average temp over the globe) since we started pumping.
Vs
Sometimes the earth goes through hotter periods.
Is it a coincidence or not?
If you're a denier, you go with the coincidence.
If you're balanced and intelligent enough to understand statistics, you might ask the question "How likely is it that we are going through a natural hotter period?"
If you're into science, you probably trust that that type of question has been posed and found to be statistically unlikely by looking at various factors.
And if it is statistically unlikely that it is just naturally hotter, aren't we essentially fucking idiots for putting our heads in the sand and ignoring it?
That's the problem. What we are being told is that it is statistically unlikely that the very true fact that earth has been getting hotter (on average).
Our choice is simple. Hope that it doesn't have something to do with us or pro-actively seek to ensure that it doesn't have something to do with us.