No, it's not true. There are many luxury car makers who are plenty profitable. If you make a huge profit on each vehicle and you can cover your fixed/development costs then you're golden, regardless of volume. At low volume that typically means higher profit margins, but that's nothing new. Companies like Maserati, Aston Martin, and Lambourghini have sales volumes in the 1-2k per year range. Companies like Bugatti are lucky if they break 100 car sales a year.

Obviously Tesla isn't quite in the same market as those companies but that still demonstrates the point.

If you have a sub-$100k car then you generally do want higher sales volume in a fleet. If you look at, for example, Audi they have a mix of cars at a variety of price-points, which enables them to amortize development costs of shared components. That effectively raises the profit margin on their luxury margins (since the development of stuff like the frame, most of the engine, etc. is payed for by sales of the down market models).