The sentence can be simplified to produce the form:
"The presence does reduce..."
which changes the meaning somewhat, but not the structure. This should make it clear why "reduces" doesn't work: you can't say "The presence does reduces".
You could alternatively say:
"The presence of a suspending medium achieves more than simply reducing..."
"The presence of a suspending medium achieves more than simply reduction of..."
I think the fact that "achieves... reducing" sounds a little better than "does... reducing" indicates that the mind treats "does reduce" as a compound verb despite the presence of intervening words, whereas it treats "achieves" as a standalone verb, which takes a gerund or noun as a direct object.
By contrast, in "He does more than he tells people", "does" does not act as an auxiliary, but as a standalone verb. Thus, the subject needs to be repeated before the second verb, and the verb is in the third person singular.