So if I buy an alternative flight myself and LH reimburses this alternative flight, it's like if they had offered me rerouting?

And then, I see in Article 5: Passenger has the right to compensation, unless they are offered re-routing, allowing them to depart no more
than one hour before the scheduled time of departure and to reach their final destination less than two hours after the scheduled time of arrival.
-> So this would mean no compensation since I arrived only 1 hour later at my final destination

Article 7 says: EUR 250 for all flights of 1 500 kilometres or less, when passengers are offered re-routing to their final destination on an alternative flight, the arrival time of which does not exceed the scheduled arrival time of the flight originally booked by two hours, the operating air carrier may reduce the compensation provided for in paragraph 1 by 50 %
-> So this would mean 125 EUR compensation

Isn't this contradictory?