When is a Dex check not really a Dex Check?

[behemoth]

I am playing a factotum and will soon reach 3rd level when the get the Brains over Brawn ability.

Definition:
Brains Over Brawn (Ex): At 3rd level, add your Intelligence bonus as a modifier to Strength and Dexterity checks and all skill checks that are Strength and Dexterity related.

So the Skill checks are pretty straight forward. What isn't (at least to me) is what constitutes a Dex and Str Check.

I assume it would apply to the following:

Str. Check for breaking down doors/barriers
Opposed Grapple checks (But not the touch attack)
Bull Rush
Overrun
Trip (But not the touch attack)

These are the two that I am not sure of:

Initiative Check
Reflex Save

What are your thoughts on these two? Are there any glaring omissions that would be useful? My PC is basically going to be an Int based fighter. He has the Improved Disarm and Trip. I am thinking of including the Improved Unarm and Improved Grapple as well. I am assuming that if I find a Magic Item that increases Str or Dex and one the increases Int, this ability would effectively stack them. (i.e. A Headband of Intellect +4 and Gloves of Dexterity +4 would effectively give me a +4 (+2 and +2) to my initiative, all my dex skills amd my reflex save?)

Thanks,

[erian_7]

By the rules, an ability check is as follows:

SRD wrote:

ABILITY CHECKS

Sometimes a character tries to do something to which no specific skill really applies. In these cases, you make an ability check. An ability check is a roll of 1d20 plus the appropriate ability modifier. Essentially, you’re making an untrained skill check.

In some cases, an action is a straight test of one’s ability with no luck involved. Just as you wouldn’t make a height check to see who is taller, you don’t make a Strength check to see who is stronger.

By this definition, some of the above are not actually Strength or Dexterity checks, as follows:

• Str. Check for breaking down doors/barriers (correct)
  
• Opposed Grapple checks (incorrect--this is a specific, known check ("grapple check") with listed modifiers like Size)
  
• Bull Rush (correct)
  
• Overrun (correct)
  
• Trip (But not the touch attack) (correct)
  
• Initiative Check (yes, as the rules specifically state "An initiative check is a Dexterity check.")
  
• Reflex Save (no--this is a specific, known check)