A lot of pediatric dentists have this policy, probably from experience of having stressed out parents panic their children unknowingly.
If you aren't comfortable with it, though, you should find a dentist with a different policy. My daughter went to one with this policy (her cavity came when she was two), but we moved her to a different dentist, and he's great with any arrangement I decide on... and he's my dentist, too! That made me more comfortable overall.
Good luck with the cavity... it happens to some children... it happened to me as a child. The only real concern is when adult teeth are coming in. Be sure the dentist is watching to make sure the tooth comes out properly. When I was a child, I had a capped baby tooth, and when the time came for the adult tooth to come, the little one wouldn't budge. It had to be extracted. Most teeth cooperate nicely, though... my experience was a rare one.