I would presume that someone like Beiber has the fancy lawyers most people don’t have; they could raise objections like demanding some indication that there was even a close encounter of the 4th kind. They could raise all sorts of objections:
The guy’s only in town for the one night, does the doctor ultrasound indicate the conception date is close enough, blood types would have to be consistent, was there any opportunity for the two to be alone… It’s not like a celebrity would wander off and get personal alone time with nobody noticing, who saw them togther, where and for how long, etc.
OTOH, the majority of men sued for paternity have some connection to the woman - the timing may just be off or they are part of the crowd. Once you admit the possibility that some alone time could have happened, the simplest solution is to give a sample.
Reading a while ago about complaints over California’s antiquated 2-year rule: if you fail to contest a paternity allegation in court within 2 years of it being brought, it’s settled and not even a DNA test can undo the finding. This goes back to the days before they had definite DNA tests - it was meant to prevent men from contesting the finding and support over and over again or shopping for a sympathetic jurisdiction.
One fellow mentioned how a crazy ex had named him father even though they hadn’t “been together” over a year before the child was born. When the court papers arrived in the mail, his current girlfriend had gotten mad and tossed them in the garbage without telling him. When he started getting dinged for support by the California Welfare department a few years later, he found he had no grounds to contest the order. A group trying to get the law changed mentioned many similar cases. Obviously a lot of fathers don’t want to be found, but the department in charge of paternity cases seemed to spend very little effort trying to properly locate and serve papers. Some were mailed to long-outdated license addresses (not even current license) or other obviously incorrect addresses. It did not matter - if the father did not manage to find out about it and show up in court or contest the judgement within 2 years, he was on the hook for the next 18. Whether the mother wanted support or not, if she collected welfare (a) she was forced to name the father (a father) and (b) they went after that father for support payments to reimburse welfare spent. IIRC, if the father contested and demanded a DNA test, then he paid for the test if it turned out he was the father. Legal tests with trail-of-evidence and trained impartial observers taking samples are more expensive than DIY home tests.
To answer the OP, basically if she named him father and brought a paternity suit, he either submitted to a blood test or forfeit the case. I assume if the judge believed the father’s story that it was a case of celebrity stalking, then he would ask for more evidence that any encounter took place. If you are just Joe Schmoe, a blood sample is quicker and cheaper - after all, it’s one of the rare situations where a legal matter can be solved with a simple scientific test (unless you have an identical twin brother).
I assume this is not a lot different than any other lawsuit. If I sue claiming your noise pollution is ruining my health or you failed to make good on a business deal or whatever, and the judge lets the case go ahead, then you pretty much have to answer in court, do depositions and the whole thing whether it’s real or fabricated. If you can afford a fancy lawyer, he might be able to properly argue the case has no merit beofre it gets too far.