No it doesn't. You're reading the English translations, not the Arabic:
http://www.speed-light.info/miracles_of_quran/Quran_18.86_sun_setting_muddy_spring_murky_water.htm
18;85-86
"So he followed a way, Until, when he reached the setting of the sun, he found it in a spring of dark mud, and he found near it a people."
The second underlined part is referring to the first underlined part. The bold part is not referring to a location, but a time of day, (when the sun is setting). If you read the link, it explains through the correct understanding of Arabic grammar why this is the case.
Dhul Qarnain followed a way, a road, that went into a muddy spring, and this road was near some tribe. The time of day when he was walking in a muddy spring was when the sun was setting. English translators add the word "place" in the verse to make it look like the muddy spring was a LOCATION where the sun was setting, but the word "place" is not present in the verse! The setting of the sun is referring to the time of day when the messenger followed a way which converged into the muddy spring. The word used in the Arabic is "Maghrib" which ALL MUSLIMS around the world know is a time of day. They even have a prayer called Maghrib prayer, which is performed when the sun is setting. So the mention of the sun in this verse is referring to the time of day, not a place where the sun actually sets.
The Qur'an already provides verses elsewhere of the motions of the planets and stars and their orbits. The Qur'an also confirms the sun goes around the round earth.