Technically every creature in the game has Hit Dice.
Psicrystals have their master's number of Hit Dice, therefore, being intelligent creatures, they receive 1 feat at 1st HD, 1 feat at 3rd HD and 1 feat each 3 HD thereafter.
Hit Dice: As master’s HD (hp 1/2 master’s)
While you do change some of the statictics as listed in psion class description, no HD change is mentioned.
The consequence of psicrystals having quite a bit of feats is maybe unintentional, but nevertheless logical implication of them having hit dice and being intelligent.
In my practice several DMs houseruled this out, without any arguing on the player's part, and I myself allow it.