"Whom" does not necessarily need to have a preposition preceding it. You can have something like "Whom did the dragon eat?"

In addition to the rule by dragon96, another useful rule is to determine if the thing referred to (in this case, the "blank" for whoever/whomever/who/whom) is the subject of any verb. If it is the subject of any verb with a tense, then use who. If not, then whom.

In both cases, the objects referred to were in dative and ablative forms (in other words, not the subjects), but were both the subjects of the verb "are", which means who is to be used.

As a very good Latin student, I shall proceed to tell you what I know.

1. If it doesn't sound right, that doesn't mean it's wrong.

2. Let's translate into Latin, which is much more structured than English, in which everything has to agree, so we must be able to figure it out in Latin..

They give knowledge to people who/whom are old. (I changed it so my vocabulary covered it, but it's the same as the little league sentence, pared down.)

Eis scientam populo dant(they give knowledge to people), qui/quibus sunt senes/senibus.(who/whom are old/old.)

Now we know that we have two clauses, because we have two verbs. These are give and are.

We also know that the relative pronoun (who/whom/which/what/etc) functions in its own clause with its own case, but match to its antecedent in gender and number. This is what you're getting confused about; you are correctly identifying that the pronouns are referring back to an objective antecedent, however it functions in its own clause.

The clause in which our relative pronoun is, is "who/whom are old". We know that "are" is a linking verb, so both nouns/adjectives on either side are nominative, or subjective. Who is the nominative form, or the subjective in English, so we come to a conclusion to use Who.

Eis scientam populo dant, qui sunt senes.
They give knowledge to people who are old.

Also this sentence:
Slow runners perform best with people who/whom are fast Rubik's Cube solvers.

We quickly see that it must be who since "are" is a linking verb, and both sides must be subjective.

Here's a trickier one in which we do not use a tell-tale linking verb:

They are kind to those who/whom give them presents.

We split them up into their clauses, and the one with the relative pronoun is "who/whom give them presents." We can identify the relative pronoun as the subject, so once again, it is subjective.

How about this one?
They are sympathetic to those who/whom their cat bit.

Now we have to split it up again: the one with the relative pronoun is who/whom their cat bit. Rearranging the clause, we get their cat bit who/whom. We quickly see that it is the objective/direct object of the clause, therefore it must be whom.

Notice in that all these examples, we don't worry about the antecedent. We worry about its function in its own clause.

I hope you get it now! Thanks for reading.

More practice? Sure.
The cat pawed at Robert, who/whom was extremely annoyed.
They give classes only to individuals who/whom were once involved in Little League.
I gave you this present because they, who/whom they invited to the party last night, gave me a present.
When you opened the present, Gertrude, who/whom became your stepsister a month ago, grabbed it and ran away.
I must tell you what it is now, since Gertrude, who/whom they covered in ice cream the other day, stole your present.
If there's anyone listening, who/whom might have been invited to the party, tell me now.
Who/Whom did you hear?
Your present was a ticket to see William Bortro at the circus, who/whom you have hugged.

Another fun Latin fact: i.e. vs. e.g.
i.e. stands for id est, or that is.
e.g. stands for exempli gratia, or for the sake of example, or more commonly used as examples are:

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