Training Grounds has an optional cost reduction ability, as indicated by the card-specific ruling:
You may choose not to apply Training Ground’s cost reduction effect. You may also choose to apply only part of it (causing an activated ability of a creature you control to cost just {1} less to activate).
Why is this conditional? Training Grounds never co-existed with Mana Burn. Are there any situations in which it would be advantageous to not apply this ability?
(This is related to Paying more mana for a Flashed creature, but is about why you would not apply the cost reduction rather than whether or not you can.)