It’s NOT the law to allow them into the country as the Biden Administration is doing. We are under NO obligation to let all these people into our country even if they do wish to say that they are here to claim asylum. This was noted from the link in the OP, which I’ll post again:
i. A state’s right to offer asylum is well known in international law. It follows from the principle that each sovereign state is considered to have exclusive control over its territory and, consequently, over persons present in its territory. One of the implications of this widely accepted rule is that each sovereign state has the right to grant or deny asylum to individuals within its borders. In international law, therefore, the right of asylum has traditionally been seen as the right of a state, rather than the right of an individual.
The Biden Administration has literally turned this around and wants us to believe that all these people who say a few magic words then have every right to be allowed into the US and wherever they wish to go. The proper procedure would be to detain them in designated facilities, or as Trump did to have them wait in Mexico until we could adjudicate their claims.