Didn't know about 'лазить' and 'ладить' , interesting. Even the stress on лажу is the same.
I found the sentence on a site as an example of correct use of a verb of motion. I suppose it would work if a climber was pointing out to his friend the route he wants to take up a mountain, saying '... сегодня я не полезу туда, но туда.'

I expected it to have the context of, maybe, a soldier refusing a command to scale a wall, saying to his seargent 'Я никогда не буду делать это', which is why it seemed wrong to me. A failure of imagination on my part, perhaps?