xph p65; The manifestation of powers by a psionic character is considered a psi-like ability, as is the manifestation of powers by creatures without a psionic class (creatures with the psionic subtype, also simply called psionic creatures).
It then goes on to say that psi-like abilities are like powers, but don't use XP, whereas powers do, which is confusing as a power is a psi-like ability, but is a power... a loop we have to ignore for fear of blue screen of death.
In any case, that's the important bit.
I can't find the reference for Psi-like abilities being able to use feats that apply to Spell-like abilities right now. I have one that specifies Quicken Spell Like and Empower Spell Like can be targeted, and I'm pretty sure that they are the only ones in core. I'm sure I've seen it though.
The tricky part comes in claiming that the Spell-like ability is "Innate".
The Warlock used to try and use this feat, and WotC website had an article or two dedicated to having fun doing so, but an FAQ was quickly released to stop it, because the warlock's description said
cArc p.5 "By harnessing his innate magical gift through fearsome determination and force of will"
, and they argued that his class feature's power was not his innate gift, but the harnessing of it.
However,
from the xph p.4 "A psionic character is blessed with a form of innate ability that enables him or her to use mental power to achieve goals or perform tasks that nonpsionic characters can accomplish—if they’re even capable of doing them at all—only by using gross physical skills such as brute strength or raw agility, or by using intellect or force of will distinct from the natural power of the mind itself."
No harnessing involved, in fact, it looks like this was worded directly to combat such an argument being levelled against us wanting to do the same.