Yes, but he did not just say "we should be able to measure gravity" in isolation. This is just one of the sentences of an article. You cannot just take this sentence and ignore the rest of the article.
As T. Quinn himself says, there have been many experiments that have measured gravity. The problem is that the results of these experiments differ by up to 450ppm and he believes that they need to do better than that.
Just read this:
https://www.nature.com/articles/nphys3651?proof=tAmong other things he says "Who needs a more accurate numerical value of G (the current recommended value6 is 6.67408 ± 0.00031 × 10−11 kg−1 m3 s−2)? The short answer is, nobody, for the moment, but being apparently unable to converge on a value for G undermines our confidence in the metrology of small forces".
He clearly speaks about an unsatisfactory level of accuracy in the measurement rather than an inability to measure at all.
Edited to correct a spelling error