There is a linguistic concept called evidentiality that describes the source or authority for a statement. All languages have ways of indicating this, but in some languages it is grammaticalized and a mandatory part of some or all statements. In English, evidentiality is not grammaticalized and must be expressed through a variety of expressions. In Latin, it is grammaticalized in indirect statement.
Consider the sentence
He said that Brutus is the one who killed Caesar.
In English, this sentence is ambiguous.
It can mean: (1) "According to him, Brutus is the one who killed Caesar" or possibly "he alleged that Brutus had killed Caesar. These are probably the default interpretations. In Latin, this might be: Dīxit Brutum esse quī Caesarem occīdīsset.
The sentence above can also mean: (2) "Brutus is indeed the one who killed Caesar, and he said so too" or, possibly, "he confessed that Brutus is the one who killed Caesar." In Latin, this might be: "Brutum esse quī Caesarem occīdit dīxit." The intonation would normally disambiguate the sentences in English, but the mood does so in Latin.
Sentence (1) makes only one assertion, which is that "he" said that Brutus killed Caesar. The author takes a neutral stance on whether or not Brutus was actually a killer. Sentence (2) makes two assertions: (a) Brutus killed Caesar and (b) "he" stated this fact. The author does assert that Brutus was a killer, but is mainly asserting what "he" said about this fact.
Latin has two main ways of expressing this neutral stance to whether something is a fact: the accusative-and-infinitive construction and the subjunctive. The use of the former is obligatory by the nature of indirect speech. The use of the latter depends on whether the author needs to make a separate assertion of fact or not.
The default in indirect speech is that the veracity of everything in subordinate clauses is linked with the authority of the person to whom the indirect statement is attributed. This default is what Allen & Greenough are expressing by saying: "ALL subordinate clauses take the subjunctive...." When the pragmatics make it important for the author to separately state a fact, the indicative must be used. These latter occastions are what they term "exceptions" to the rule.
In the clause "by whose genius he thought that those deeds which he had done could be celebrated," the author is only attributing the appropriateness of the celebration to the speaker and does not want to put in question whether the deeds occurred or not. As a result, the author uses the indicative for quae gesserat to separately assert them as facts to focus the reader's attention on whether the celebration was or was not appropriate. If the author had said quae gessīsset, it would lead the reader to think that the author was attributing authority for the factuality of the deeds to the original speaker, indirectly creating doubt as to whether or not they did in fact occur.
Since English has no easy was to express this difference, Allen & Greenough have translated quae gessisset as "what Marius claimed to have done," but this overstates the pragmatics somewhat. A closer translation for the full sentence might be: "by whose genius he thought that those deeds which, according to him, he had done could be celebrated."
Since pragmatics can affect whether not a subordinate clause takes the subjunctive, Allen & Greenough say the choice "often depends merely upon the feeling of the writer whether he shall use the indicative or the subjunctive." A more exact way to express this would be to say that which mood is used affects what the author separately asserts and therefore can depend on what the pragmatic intent of the author is.
[A & G appear to be contradictory in their instructions on subordinate
clauses in indirect speech: from "ALL subordinate clauses take the
subjunctive..." (sect. 580; p374) to this sect. 583: exceptions:
truth; an explanation; emphasis--take indicatives. (Wouldn't any
writer claim that his material is true; an explanation of something;
worthy of emphasis; combinations thereof? By this logic, the verbs
will always be indicative.)]
Despite what grammars say, the choice between the moods is not directly driven by "truth," "a desire to explain," or "emphasis." It is driven by who the author wants to attribute the assertion to and the overall pragmatics that may indeed be connected with "truth," "a desire to explain," or "emphasis." When an author fails to accept authority for a statement, this can create an implication that the underlying truth is in question; however, this is merely a social implication.
For instance, if I say "Country X launched a satellite, which was apparently for peaceful purposes," you may wonder if I have doubts as to whether the peaceful intent is true. If I said: "Country X launched a satellite, which was for peaceful purposes," you know that I believe the explanation. If I said: "Country X launched a missile that was the first threat to world peace," you know that I am emphasizing my opinion about the reality of the threat. If I said: "Country X launched a missile that was said to be the first threat to world peace," you don't know what my opinion is about the reality of the threat. In Latin, these nuances are mostly expressed by the choice of indicative or subjunctive.
