PCR tests are not unreliable or prone to false results (I am a PhD who is active in this field). The tests that do not work well are the 'rapid tests' that attempt to detect antibodies in blood. You're better off flipping a coin.
This was a false alarm and is not true. The government announced yesterday that things are to remain as-are until (likely) October 1, 2020, at which point, there will be a mandatory 14-day quarantine for all travelers from high risk countries (as per the official list from the Robert Koch Institute on that particular day), UNLESS a negative COVID-19 test is obtained after entering Germany (no more pre-travel testing). The likely policy will be a mandatory 5-day quarantine for those who test negative, which kind of makes sense since getting tested immediately after an intercontinental flight is unlikely to detect a very recent infection.
Summary: from October 1 there is likely to be a mandatory 14-day quarantine for travelers from high risk countries, 5-day quarantine for those who test negative after arriving in Germany.
