I'm no math major but you can't cut a fuel bill in half AND spend more per gallon unless you more then double the MPG. So she may be saving some (not double) she could have also spent less money on a new gas car that also gets 40, or even a 96-99 manual DOHC neon that gets over 40 and is quicker then any TDI. So getting 41mpg with $3.10 regular is much better then 46MPG with $3.80 diesel.
The neon costs $37.80 to go 500 miles and the TDI costs $41.30.