Do you really get 30,000 CP for each fragment?

This is a quote from this website:

Final Fantasy 13-2 doesn’t really require much grinding compared to Final Fantasy 13. You should be able to level up each role to 99 just by collecting all fragments (See fragment Locations). Each fragment rewards 30,000 CP and collecting all fragments rewards you with Defragmented trophy so it’s worth the effort.

Are they telling the truth? Can you really get 30,000 CP just from getting one fragment?!

Each of the 4 bosses in the Archlyte Steppe AF yields 30,000 CP.

Their claim is that each fragment gives you 30,000 CP: from my experience after collecting 120 fragments, only the four big game monsters (Ochu, Shaolong Gui, Immortal, and Yomi) and completing the game awarding 30,000 CP.

Additionally, paradox ending fragments each award 10,000 CP.

Most other fragments are usually the rewards for completing a side quest: the CP bonus you receive is just a quest reward and is somewhere between 200 and 1,000 CP. If you want to max out your crystarium grid (and your monsters' crystarium grids using monster materials), you'll be doing some grinding.

So while you technically can get 30,000 CP from a fragment, the site is indeed mistaken as there are only a small number of them that give that type of reward.

The site also claims each battle awards 1,000 CP off the bat: that's not even close to being correct. In first few areas, battles award something in the 25-100 CP range. The question about grinding has answers suggesting grind-worthy mobs cap out around 300–400 CP (which matches up with my experience), well below their claim of 1,000 CP being routine.