Because the use of "that" and "same...as" are two different grammatical constructions.
(a) I applied for the same company that my brother did.
Here "that" introduces a restrictive clause.
I applied for the same company as my brother did.
(b) Here, the combination "same...as" is used to say that two things are equal in some way.
The above two grammatical structures are different.
But (a) only looks similar to (b). And (a) does not have to have the word "same." So, we could have
(c) I applied for a different company ____ my brother did.
Which one do you think is correct here? Think: if you use "that" you are making a restrictive clause "that my brother did." If you try to use "as," you are trying to say two things are equal in some way.
Again, you can have:
(1) She thinks the same as I do.
Reason: "same...as" = two things are equal in some way
But you cannot say:
(2) *She thinks the same that I do.
This is incorrect grammar.
But you can say:
(3) She thinks the same things that I do.
Here, "that" introduces a restrictive clause.