You don’t seem to understand what the study you are criticizing did.
They weren’t just measuring temperatures for a given moment in time, they were comparing temperatures OVER time. So, they’re comparing all the current data to all the old data, which means you need to use both types of data. Unfortunately the differences in measurement technique matter because of how statistics (look up standard deviation) works when you want to federate two different data sources, so you need to normalize one to the other. It doesn’t matter whether one is more “accurate” (you really mean ‘precise’ in scientific terms) because you need to use both data sets.
So, with your baby example say you have some precise rectal readings from a group of babies, but you think babies are getting hotter over time, so you want to see if your current babies are heating up in the same way they have in the past. You’re not comparing absolute temperatures, you’re comparing CHANGE, so you don’t really care what the number is so much as how much the number changes. You also know that rectal readings run hotter than skin readings, but all your readings in the past were skin readings. If you just added them together you’d add a pile of variability because of the differences between the two data sources. So what you’d do is normalize one data set to the other so your SD is under control and then look at changes from your baseline.
This isn’t some sort of radical idea, it is the way ALL science is done that requires federation of this kind. The MRI example is an excellent one. Different MRIs produce different numbers. They might both be precise, but if you add them together without correction you’ll just get noise. Which actually has been a big problem in the imaging literature. If you look it up you’ll see that standardizing these kinds of correction factors is a whole topic of debate in the imaging field, with the field being extremely critical of those who didn’t do it right.
The NOAA have posted their methods online as well as in their excellent paper. There is nothing untoward about what they did. You should actually read their paper before you criticize it.
