The point is that they've established a relationship between o16 levels and temperature, so if you've got twice the o16 then say it was 25% warmer (made up ratio, I haven't read the study).

This doesn't tell us what the air temperature was, but it does tell us what it wasn't (IE upper and lower bounds).

When you have several of these proxies it helps narrow down the temperature range (think how your god works better when you have more satellites).

Now if you know that the last seven days are the hottest on record and you know from your proxies that you are outside of temperatures of the past 100k years then it's a pretty safe bet to state that we're at the hottest time in the past 100k years.

There is no melodrama or lying in this fact, unfortunately.