Change the meta? Yes. They do, but not directly. It happens when something prevalent is strong, they nerf it, and then something else takes over. Example: ADC prevalence, when Crit was nerfed, Lethality ADCs became a thing because the playerbase found it more effective. Did Riot's nerfs cause a change to the Meta? Yes. Did they look at the game, think "We want a Lethality Meta" and then nerf crit expecting that to happen? No. That came out of left field.
The playerbase is largely responsible for the actual meta, because they innovate and figure out what can become viable. What can become meta, is largely responsible on Riot's changes, from nerfs and buffs. If something is too strong, it'll get nerfed, and then something new will come out as the newest strongest thing, and then that will be nerfed.
Riot can affect the meta, but they do not look at the game, and say "Yes, we want this meta." Game state/length is not the same as Meta, but it can help affect the meta.