It's complicated. The reason *whom* is wrong is that it's not an object; it's a subject.  
It just **looks** like it oughta be the object, but only if you don't know the syntax.  
That's what makes it a great test distractor. Here's the example sentence, stripped of irrelevant details.

 > 1. *They **interviewed** several candidates*  
2. *who he **thought***  
3. ***had** the right experience and qualifications*  


3 main verbs, therefore 3 clauses: 
  
 - (1) is the main clause, and has the statement in it.  
 - (2) is a relative clause, modifying *candidates*.  
 - (3) is a _that_-less tensed complement clause, the  direct object  of *thought*.  
 
Note that (3) is subjectless, though it's clear that its subject refers to whoever _who_ refers to.  

So the question is, why is _who_ correct? Because it really **is** correct here, and *whom* is incorrect.  
(one more example, by the way, of why I tell people never to use *whom* at all; *who* is alway safe)

Let's take a look at some other sentences. Let's start be deleting "he thought", producing

1. *They **interviewed** several candidates*  
2. *who **had** the right experience and qualifications.*

Note that _who_ is in fact the subject of *had* in this relative clause; *whom* would be wrong.  
And another sentence:

1. *I think*   
2. ***that** they had the right experience and qualifications.*   
  2'. *they had the right experience and qualifications.*

Clause (2) is tensed (it's in past tense; it's not an infinitive or gerund), it's a [complement clause][1] (the clause is the direct object of *think*), and it starts with the complementizer *that*, which is optional here, as (2') shows. 

So what? Well, one more fact about tensed complement clauses: 

 - a tensed complement clause with *that* is [an island][2], but without *that* it's **not** an island.

And two more facts about relative clauses: 

 - relative clause formation can extract relative pronouns from **far** away in the clause   
(*several candidatesᵢ **whoᵢ** had the qualifications*)  
(*several candidatesᵢ **whoᵢ** he thought had the qualifications*)  
(*several candidatesᵢ **whoᵢ** she said he thought had the qualifications*)  
 - **but** they can't extract them from islands; add *that* and it becomes ungrammatical.  
(*_several candidatesᵢ **whoᵢ** he thought that had the qualifications_) 
 
What that adds up to is that the relative pronoun heading a relative clause may come from indefinitely far away, and does not necessarily have anything to do with the clause that happens to be at the beginning. 

In this case, the *I think* part is essentially an adverb and adds no information, but instead qualifies the speaker's assertion. It plays no part in the rest of the relative clause, and its object is a whole clause, not a pronoun. *Who* was extracted from the subject position of that object clause and moved to the front by relative clause formation.

  [1]: http://www.umich.edu/~jlawler/Complements.pdf
  [2]: http://www.umich.edu/~jlawler/aue/ross.html