Depending on where we look, the universe is expanding at different rates. Now, scientists using the James Webb and Hubble space telescopes have confirmed that the observation is not down to a measurement error.
From my limited understanding, the discrepancy comes from the two ways to measure the universe's expansion: calculation from cosmic microwave background and calculating a cepheid variable, which uses pulsating stars (pulsars?)
Isn't it more likely that one, or both, ways of measuring are wrong? As in, they're not useful for measuring the universe's rate of expansion?
Pretty much this. In a (hopefully) more direct metaphor, are we sure we're using a ruler to calculate the length of a line, and not using a ruler to calculate the temperature of a paper?
I think the distinction is between arguing that there's a discrepancy because the measurement is bad, or because the measurement doesn't measure what we think it measures.
Is the theory right and we have a measurement error, or is the theory flat out wrong?