No! It not true, a lot of cheap amulets do work very well.
The price doesn't matter, the power in the amulet does not base on the price.
It depend on the creator, if the amulet is created by the great guru monk who has spiritual knowledge skills, he would invite the Buddha’s and deities, and perform
blessing ritual with chanting making the amulets Holy and Potent.
If you would like to collect the newly-made amulets, you should know some of
these questions: who create it, from which temple, who are invited to perform the blessing ritual ceremony, and what are the purpose for creating the amulet, etc.
In the old times, actually amulets were created to devotees as a gift in exchange
for their helped and supported on their temple development.