In the case of illegal immigration, expedited removal [1] was established in 1997, under Clinton. It qualifies a number of different groups for immediate deportation without a hearing, including anybody who has been in the country for less than 2 years - which would include the individual in this article.
And how would you know if they've been here for less than 2 years without a hearing where they can face their accuser and provide any evidence they have to refute it if untrue?
That doesn't mean you don't have due process to establish that the individual was actually undocumented. You don't skip due process. What's so hard about that? What if the individual is actually in the country with all of the correct paperwork and visas?. That's what you figure out via due process before acting.
Non-citizen residents in the US are required to carry proof of immigration status with them at all times, precisely because of this scenario. Immigration officers/enforcement, in basically every country, have a substantial degree of independent discretion.
Indeed, US has a longstanding problem with due process for non-citizens. Trump's embrace of it is qualitatively different but the seeds have been sown a long time ago.
[1] - https://en.wikipedia.org/wiki/Expedited_removal