The odds of two units derived independently being interchangeable to infinite precision with just two decimal places seems unlikely, so I'm guessing that at some point one unit was slightly modified to match the other. When did this happen and which unit was changed?
The definition of the inch was set to exactly 2.54cm starting in 1930 (the UK) but wasn't adopted by all countries using inches until 1959. The nominal length of the meter has never changed (although the exact way the standard is defined has). They were able to choose a comparatively round conversion ratio because surprisingly, unlike metric units, prior to that the inch had not been universally defined in the same way. So if you're going to compromise, and all the numbers are very close to 2.54, why not just make it an exact 2.54.