Define accuracy…

[TL/DR] Good estimates is absence of other data but open to nit-picking

One of the primary uses of oxygen isotopes is for a proxy of environmental temperature at the time the ice was deposited, since there is no historical weather station data reaching back hundreds of thousands of years.

Primarily this is a measurement between O-16 and O-18. In a sample. (This ratio can also be measure in seashells of very small marine animals) Neither oxygen isotope is radioactive so that variable is eliminated.

Because O18 is 1.125 x heavier than O16, this makes for slight physical differences between water made of O16 and O18. Think boiling point and vapor pressure.

It turns out that evaporation and sublimation very slightly favors O16 water molecules leaving and O18 water molecules remaining behind.

This is know as fractionation and fractionation is temperature dependent.

The relative abundance of O16/O18 in a sample can be measure with precision in a laboratory and so there is good, reproducible data documenting the ‘curves’ in the lab.

The environment is much more complicated, for example during ice ages more O18 water might be locked up in massive ice sheets leading to some skewing of the temperature estimates. The magnitude is the skew is a function of your assumptions about ice volume and such. Regardless, the estimated local environmental conditions based on Oxygen isotope ratios give a valuable albeit imperfect proxy of the temperature when there is no other data.