I have the impression the downplaying is the major trend in Europe as well, so no, it’s not something limited to the Trump administration.
It is telling that Taiwan, which is super close geographically and culturally to China has now less cases than Italia, France and Germany. I’ve been there at the end of January when the thing started to be on TV and the difference in gov and public reaction with my country is huge.
Taiwan: 99% people outside wearing masks starting from the first days, government putting money to open a new mask factory, mask rationing so that they are available with healthcare card, some people limiting their move, people putting themselves in quarantine when coming back from China.
France: every media and the government saying there is no problem for more than a month, even when a close European country closed some schools. People going their live as usual even in regions with lot of cases. No quarantine, no border control. My family reaction: the virus is overrated, complaining about events cancelled (the trend just started this week), goes to public events even now.
Japan: government and people actions in-between West and East. Japan handled the ship semi-seriously, yet started taking other measures really lately. People bought every masks and toilet paper rolls out there, government did nothing so that we can each have some. Gel available at most shop or public place. Some information here or there about the importance of washing hands.