No, I do not think so.
What makes it alright that you can get higher bonuses (Weapon values for example) due to certain equipment and not get higher bonuses due to other equipment?
If you have a handgun and load it with hollowpoints to do more damage(for example), why should you have to invoke the hollowpoints every time you fire the gun? How does a scope aid in hitting a distant target when you spent a Fate point and how does it suddenly not when you don't?
*sigh* If you're really that bothered about it, house rule it - up the base damage of the weapon by one level or something similar and stop worrying about the fine details. The weapons damage ratings are hazy and not really meant to model reality, I assume because the game writers didn't really want to have people bogging down the story obsessing the finer details of one hand gun over another, and one type of ammunition over another.
Given that you don't actually hit an opponent until you've inflicted a consequence, you could probably just word the consequence appropriately to the type of ammunition used. Like I said, the weapons base damage are hazy and meant to represent an average weapon of that type. I don't see the need to complicate the system by bringing in extra rules to cover variations on each weapon.
My view is that what you're trying to put in there is a situational modifier, which in Fate is replaced by aspects. By all means do what you like, you'll never play in one of my games I'll never play in one of yours, so does it really matter? But if you're after all those juicy modifiers due purely to bits of equipment then you're probably actually wanting a different system. Fate's designed as a very basic system that puts story over intricate combat mechanics that account for every eventuality and piece of equipment. Maybe you'd be better off with something with weapons tables, accuracy modifiers and recoil penalties.
To answer how a scope aids your shot when you use a fate point and doesn't when you're not - the simple justification is that if you don't invoke the scope aspect, you're either not using it effectively, or not using it at all. Given that it's laughably simple to justify use of the sight giving you a bonus by simply using maneuvers to place the aspect 'IN MY SIGHTS' on a target - which gives you a free tag on your first shot every time you do so, I still don't see the need for adding in any extra bonuses.