People are offering to buy their own ticket, but no they're sent to detention for no reason, at taxpayer expense.
People are offering to stay private, but no they're sent to detention at taxpayer expense.
A Czech woman is being sent to Mexico instead of allowing her to pay herself to fly home to Prague.
All this spending of UK taxpayer funds for what? Out of spite?
It's annoying and slightly weird, but isn't that just how it works? You go 'back where you came from', not wherever you want or claim to live?
Say the woman in your example was refused by Czech customs, and sent back to the UK, then what? Dig through records (would they have them?) to find she came to the UK from Mexico, and then send her there?
Correct me if I'm wrong, I just don't think that would be different in any other country. (That particular aspect I mean, assuming they've decided you're not allowed in, and will be deported to somewhere.)
Considering she is Czech, she is far more likely to be rejected by Mexican customs rather than Czech customs.
Unlike the EU, where about 30% of illegal immigrants are expelled, while no one no one is interested in changing that legal status.