I'm 5'8" and ride a 20 inch or 52cm or so frame.
Ditto on the seat-height and toes-on-the-ground.
I can touch the ground (just barely) with my toes while in the saddle, but that is because I have the saddle slightly low and shoved back to compensate for a bad knee. If I had the saddle adjusted "normally" there is no way I would be able to touch the ground while on the saddle. Generally, if you have the saddle set so you have only 10-15 degrees of knee flexion when your leg is straightest, you are in the ball park. (I get that because having my seat back farther puts me farther away from the pedal even though the seat is a smidge lower than text-book height for my inseam.) There are lots of other fine-tunings for saddle placement, and I would imagine she'd be able to get a 20 inch to fit pretty darn well!
Most folks prefer to get off the saddle and be weightbearing on one pedal (imagine using the pedal as a step) before they stop and need to touch the ground. Scooting around while off the saddle and using one pedal and the bars to control the bike is a pretty nifty bike handling exercise, too.
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson