15 Ampere cord-and-plug appliances can indeed, safely be connected to 20 Ampere receptacles.
A deeper understanding
NEMA 6 is a design standard for three wire grounded cord-and-plug devices and receptacles. The number after the dash (-), is the current rating of the device. For example. A NEMA 6-20 device, would be a three wire grounded cord-and-plug device capable of withstanding 20 amperes of current. The "R" simply tells you that the device in question is a receptacle. A NEMA 6-20 cord-and-plug device, would plug into a NEMA 6-20R device.
The NEMA design standard is a safe and convenient way to determine what can connect to what. Basically, if it fits, it works.
If a 15 Ampere device is connected to a 20 Ampere rated receptacle, the device will still only draw a maximum of 15 Amperes. Plugging the device into a higher rated receptacle, will not cause it to draw more current.