Note it does NOT say the clouds are 50 miles up. It says “But solar-minimum conditions, with few if any sunspots, are causing cooling in the extreme upper atmosphere 50 miles high where the lowest atmospheric temperatures are recorded, approaching -150 F. That altitude is above 99.999% of the air in the atmosphere.”
So somehow the solar minimum is causing upper atmosphere cooling which is affecting clouds down below. These appear to be cirrus clouds which are made of ice crystals. Cirrus clouds can form at any altitude between 16,500 ft and 45,000 ft.
Your interpretation was correct. That is amazing to think of clouds forming at that altitude.
Wikipedia says "They are the highest clouds in Earth's atmosphere, located in the mesosphere at altitudes of around 47 to 53 miles. They are too faint to be seen in daylight, and are visible only when illuminated by sunlight from below the horizon while the lower layers of the atmosphere are in Earth's shadow...Noctilucent clouds are not fully understood and are a recently discovered meteorological phenomenon. No confirmed record of their observation exists before 1885.
"Data from the Aeronomy of Ice in the Mesosphere satellite suggests that noctilucent clouds require water vapour, dust, and very cold temperatures to form. The sources of both the dust and the water vapor in the upper atmosphere are not known with certainty. The dust is believed to come from micrometeors, although particulates from volcanoes and dust from the troposphere are also possibilities. The moisture could be lifted through gaps in the tropopause, as well as forming from the reaction of methane with hydroxyl radicals in the stratosphere.