How on earth is it possible that the difference between two temperatures in Celsius and Kelvin is exactly the same. Given the historical definition of Celsius, I find it hard to believe that this is pure coincidence.
It's because the Kelvin scale was and still is defined so that as a measure of temperature difference, one kelvin exactly coincides with one Celsius degree. So the temperature in kelvins was defined as the temperature in Celsius degrees minus $A$ where $A=273.15$ °C is the temperature of the absolute zero, without any additional multiplicative factor.
When people learned how to measure the temperature more accurately, they could have redefined the scales a little bit so that the new definition didn't depend on arbitrary constructs such as "ordinary atmospheric pressure" (which had to be imposed to define the boiling and freezing points previously). Today, one kelvin is defined so that the triple point of water is exactly 273.16 kelvins and the scale is "linear" in the usual sense (e.g. when one measures the pressure times volume of the ideal gas; absolute zero is 0 K, of course). But this is just a refinement that was designed to match, within the error margins, the previous definition based on the freezing and boiling points of water at reasonable pressures.
The kelvin is defined as the fraction 1⁄273.16 of the thermodynamic temperature of the triple point of water (exactly 0.01 °C or 32.018 °F).
Lord Kelvin (William Thomson), wrote in his paper, On an Absolute Thermometric Scale, of the need for a scale whereby "infinite cold" (absolute zero) was the scale's null point, and which used the degree Celsius for its unit increment.
This is the historical data, so yes, I wouldn't say that this is a coincidence...