Generally poverty and crime are the two that correlate heavily and so in sectors of the population where you have high levels of poverty then you also have high levels of crime which is why safety nets and welfare are so important for reducing crime.
If you think about immigration that is a subset of the population that have high levels of poverty, low levels of access to welfare and so if things go wrong they get desperate quickly. And they also have more problems than locals at getting work due to discrimination and a host of other reasons.
That might explain why immigrants in that country have higher crime rates but it doesn’t invalidate the point that cutting immigration would be one way to lower crime rates.
But it does invalidate it, as the comment does not attack the cause, it's just blaming an outcome of poverty rather than the poor. It's why often those same commentators blame the poor for being poor rather than attacking structures that continue to trap people in poverty
Cutting poverty is a more effective measure.
Actually I'll go further if you were serious on cutting crime you would be advocating to cut poverty!!
If you think about immigration that is a subset of the population that have high levels of poverty, low levels of access to welfare and so if things go wrong they get desperate quickly. And they also have more problems than locals at getting work due to discrimination and a host of other reasons.