British tourist detained by US authorities for 10 days over visa issue

Earlier this month, the Guardian also had an article of a German tourist who crossed over the land border (San Ysidro Port of Entry, I assume) who was detained for a long while too. The details seemed kind of similar to this situation where it involves suspicion of tourists working in the USA without the proper authorizations.

It seems like there was good reason for these concerns that the person was going to work. However, the person was right there at the border. Why did we not just turn them back around. I don't think they had overstayed their time in Mexico? Further they had a return flight weeks ago. AFAIk we have been paying to keep this person detained for over a month now. Why not at least put them on their original flight back. This entire approach with detention and deportations seems a very expensive solution.

Edit: In general it seems that if the goal is to reduce illegal immigration, it would be much cheaper to deter most illegal migrants who generally come for economic reasons by fining employers of workers without permits. Instead of cost it brings in money and the illegal workers will deport themselves if all work dries up.

It seems like a common detail for both situations is both travelers were at a land crossing. It sounds like a nightmare scenario but I bet they also could have been bounced back and forth between the guards of either country. At that point, one side will have to take on detention responsibilities because neither side will trust the person to make good on their return plans.