That's because Spellstrike simply replaces the free touch attack that you get when casting touch spells by a weapon attack.
All mechanics related to your weapon will work normally regardless of the spell being cast, and all mechanics of the spell will work normally regardless of the weapon being used.
Spellstrike modifies the spell, not the weapon.
At 2nd level, whenever a magus casts a spell with a range of “touch” from the magus spell list, he can deliver the spell through any weapon he is wielding as part of a melee attack. Instead of the free melee touch attack normally allowed to deliver the spell, a magus can make one free melee attack with his weapon (at his highest base attack bonus) as part of casting this spell. If successful, this melee attack deals its normal damage as well as the effects of the spell. If the magus makes this attack in concert with spell combat, this melee attack takes all the penalties accrued by spell combat melee attacks. This attack uses the weapon’s critical range (20, 19–20, or 18–20 and modified by the keen weapon property or similar effects), but the spell effect only deals ×2 damage on a successful critical hit, while the weapon damage uses its own critical modifier.
See how the spell effect actually doesn't even use the weapon's critical range and multiplier? It threats on a natural 20, and multiplies only by x2 (same as Delivering Touch Spells).
Which means that the source of this damage is the caster.
The FAQ on spellstrike clarifies this even futher:
Can a magus use spellstrike to cast a touch spell, move, and make a melee attack with a weapon to deliver the touch spell, all in the same round?
Yes. Other than deploying the spell with a melee weapon attack instead of a melee touch attack, the magus spellstrike ability doesn’t change the normal rules for using touch spells in combat. So, just like casting a touch spell, a magus could use spellstrike to cast a touch spell, take a move toward an enemy, then (as a free action) make a melee attack with his weapon to deliver the spell.
On a related topic, the magus touching his held weapon doesn’t count as “touching anything or anyone” when determining if he discharges the spell. A magus could even use the spellstrike ability, miss with his melee attack to deliver the spell, be disarmed by an opponent (or drop the weapon voluntarily, for whatever reason), and still be holding the charge in his hand, just like a normal spellcaster. Furthermore, the weaponless magus could pick up a weapon (even that same weapon) with that hand without automatically discharging the spell, and then attempt to use the weapon to deliver the spell. However, if the magus touches anything other than a weapon with that hand (such as retrieving a potion), that discharges the spell as normal.
Basically, the spellstrike gives the magus more options when it comes to delivering touch spells; it’s not supposed to make it more difficult for the magus to use touch spells.
Spell Storing: Yes
Spell Storing on the other hand, is a weapon magic quality, and does explicity say that the weapon is casting the spell stored on it, not the caster.
A spell storing weapon allows a spellcaster to store a single targeted spell of up to 3rd level in the weapon. (The spell must have a casting time of 1 standard action.) Anytime the weapon strikes a creature and the creature takes damage from it, the weapon can immediately cast the spell on that creature as a free action if the wielder desires. (This special ability is an exception to the general rule that casting a spell from an item takes at least as long as casting that spell normally.) Once the spell has been cast from the weapon, a spellcaster can cast any other targeted spell of up to 3rd level into it. The weapon magically imparts to the wielder the name of the spell currently stored within it. A randomly rolled spell storing weapon has a 50% chance of having a spell stored in it already. This special ability can only be placed on melee weapons.
Now, Foe-Bitting says:
When this item deals damage, its user can use mythic power to double the total amount of damage it deals. If the attack is a normal attack, the bearer can expend one use of legendary power to double the total amount of damage.
That clause does not specificy the type of this damage, be it the weapon's damage, or a special effect on the weapon, as long as the source of this damage is the weapon.
Rules as Intended: Yes for both.
We are talking about a Legendary Item, so simple mechanics like that should be considered as legendary use of the weapon and be allowed by the GM.
These things are one step bellow artifacts. Some are even legendary artifacts.
There is simply no mechanical, or balancing, reason to not allow that to apply to both cases, as there are more mechanical ways to get stronger weapon damage using the Mythic Rules.
Just make sure to never hand out a Legendary Scythe, or you will be asking for trouble coming your way.