Recruits are required to pass background checks. A certain percentage of recruits - citizen and non-citizen alike - don't pass. The U.S. military supposedly enlists thousands of non-citizens every year, so under normal circumstances a certain percentage of them won't pass, either.
The AP writer doesn't know how widespread the situation is and neither do the attorneys who filed suit. They know of 40 so far. One of the claims being made is that the military added onerous background requirements to immigrant recruits, and then when those couldn't be completed prior to the recruit entering boot camp they get discharged.
One of the problems the military has been commenting about is it's gang activity problem, up to and including MS-13 members getting in. So any ramp up in background screening that could be attributed to that might be justified, and might not be attributable to an anti immigrant bias.
Which, lest we forget, those people aren't even entitled to be here in the U.S. in the first place. Whatever loopholes we establish for them amount to an act of generosity on our case, not a moral obligation.
It probably won't be long before the military releases the data on its non-citizen enlistment statistics. At that point the attorneys who filed suit will be better informed as to whether their allegations have merit.