Confusing use of 'up to'

Is the use of 'up to' semantically correct?

Yes.

Or, is 'at least' more appropriate to replace 'up to'?

No.

Should it be rewritten to clear the sense in following manner?

No.

up - adverb = upwards (indicating an advance motion, place or time.)

to - preposition

to + substantive = modifier.

Up to + substantive = adverb.

You can cancel the tickets up to thirty minutes before the scheduled departure of the train.

Here "up to" means time going forwards or "until".

You can cancel the tickets any time but at least thirty minutes before the scheduled departure of the train.

Which is it? "any time" or "at least thirty minutes before"? It says one thing then immediately contradicts itself. People don't always have time to struggle through complex grammar when they need an answer to the question "Can I cancel my ticket right now?" This is a real world problem, not a thought experiment. The simplest grammar is preferable.