The planar channel uses per day aren't necessarily Charisma-dependent, but the saving throw DC is
The supernatural ability planar channel of the planes walker (né the Paths of Prestige prestige class riftwarden) says
At 2nd level, a Planes walker can channel baneful energies against creatures with the extraplanar subtype, regardless of alignment or plane of origin, as the cleric's channel energy ability. The Planes walker deals damage as a cleric of a level equal to her highest caster level. This energy can only harm, not heal. This ability cannot be used with feats, magic items, or other effects that modify channel energy. A Planes walker can use this ability a number of times per day equal to 3 + her bonus for the relevant ability of the spellcasting class she selected.
Emphasis mine. The cleric's supernatural ability channel energy says, in part, that
Channeling energy causes a burst that affects all creatures of one type (either undead or living) in a 30-foot radius centered on the cleric. The amount of damage dealt or healed is equal to 1d6 points of damage plus 1d6 points of damage for every two cleric levels beyond 1st (2d6 at 3rd, 3d6 at 5th, and so on). Creatures that take damage from channeled energy receive a Will save to halve the damage. The DC of this save is equal to 10 + 1/2 the cleric's level + the cleric's Charisma modifier. Creatures healed by channel energy cannot exceed their maximum hit point total—all excess healing is lost. A cleric may channel energy a number of times per day equal to 3 + her Charisma modifier. This is a standard action that does not provoke an attack of opportunity. A cleric can choose whether or not to include herself in this effect.
Emphasis mine. So while the uses per day is based on the text for the supernatural ability planar channel, the actual effect (except as stated) is based on the text for the supernatural ability channel energy. (Likewise the planes walker's planar scourge and planar purge abilities.)
Thus, for example, when a typical wizard takes the second level of the prestige class planes walker, he can use the supernatural ability planar channel a number of times per day equal to the 3 + his Intelligence modifier, but the saving throw DC is still 10 + 1/2 his effective cleric level + the wizard's Charisma modifier.