I have no doubt that a lot of the nasopharyngeal sampling being performed around the country is collecting inadequate and potentially misleading material.
The image embedded above is a enhanced photograph showing that access to the nasopharynx is straight back - along the roof of the mouth - NOT upward toward the brain.
The white tip of the swab in the photo is touching the nasopharynx, where Covid-19 lives. The virus may or may not also be present in the anterior nares, and I will bet a dollar to a doughnut that lots of swabs are giving false negative results because the sinus and turbinate area is swabbed, not the nasopharynx.
A full 5-minute video (from which the screencap above was taken) is available for viewing at The New England Journal of Medicine - along with detailed information about protection for the medical worker and processing of the specimen. Note for example the procedure for removing PPE optimally utillizes three pairs of gloves:
Remove your PPE as shown in the video and described here or in accordance with the standards at your institution. First, remove your gown and gloves. Clean your hands with an alcohol-based solution or soap and water. Put on a new [second] pair of gloves, and then remove your face shield and either dispose of it or clean and store it in accordance with the guidelines at your institution. Remove your gloves, rewash your hands, and put on another [third] pair of gloves; then remove your mask and follow your institutional guidelines for disposal or reuse. Finally, remove the last pair of gloves and wash your hands.