Yes you are wrong to suggest there is any controversy regarding whether or not eukaryotic cells have topoisomerase. That is a fact well-known to anyone with a basic biology education (topoisomerase “unwinds” DNA ). You are correct that this is hypothesized to be the reason that flouroquinolones have a pretty extensive side-effect profile, particularly in younger children who are undergoing more DNA replication cycles than adults. If you don’t have any medial training, then kudos to you for identifying this link and the (hypothesized) reason for it.
Every MD I know is well-aware of the side-effect profile and none of my peers regularly prescribe these drugs for this reason. This study seems to simply identify an association between neuropathy and FQ usage, which isn’t remotely interesting considering diabetes (the main cause of peripheral neuropathy) increases the risk of virtually every disease that FQ’s are used to treat. IMO, the only remotely interesting aspect is that males seemed to be at higher risk for peripheral neuropathy following flouroquinolone usage. However, males are also more likely to have diabetes so this may not be a surprising finding either.