@whatsnew,
No its not true. The LED replacement bulb will draw less current than the equivalent incandescent; which is the benefit of LED bulbs as well as their long service life. It won't hurt the transformer.
What it does mean is that you will have more capacity to add more lights with your current transformer.
I put an LED landscape light system at my house. I put in 2o path and up lights. There were a few runs of over 100 feet. I was able to buy a smaller transformer for the LED lights since they drew less current (even at the long runs) than with incandescent lights..
I have had no problems at all. Its important to get good fixtures though.