Nope, they were originally 4:3 and then remastered (re-rendered, actually, that's why they look and are native HD) to 16:9 1080p later, it wasn't until around season 13 that episodes were made in HD
It seems the United States was way behind on this one. Britain began DTV transmissions as far back as 1998 and completely phased out analogue broadcasts on a phased-by-region basis between 2008 and 2012.
HDTV actually started in the US around '99, but it took a little while longer for the general public to adapt, so we kept pushing back the analog cut-off date. Most people had upgraded to HDTV by 2008 or so.
Interesting to think analog shut off only 7 years later in 2009, when in 2002 hdtv was still in its infancy and still had to be explained to the public. That’s a big change in 7 years