Yes and no. Tune in next week when we'll be answering...Oh you wanted a little more detail? OK we can do that.
When I see the blanket statement, "Batters have little to no control over batted balls," I tend to have a conniption fit. If you've ever had a conniption fit, you should be grateful that your conniption wasn't a size too loose. What I aim to offer here is a primer on when and how a batter can, and cannot, control where and how they hit the ball.
The first good basic rule of thumb is that batters can control the macro level better than they can control the micro level. When you see an identically sharp one-hopper to 1B, sharp one-hopper to 2B, and sharp one-hopper through into RF, those batted balls are pretty much identical process, with different outcomes.
Batters can not aim for the hole while reacting to pitches of different velocities, breaks, locations, and movement; they can just try to hit balls hard enough that they are more likely to escape the range of the fielders. So whether a ground ball hit with a given force, or a fly ball hit with a certain trajectory, is an "at 'em ball" or a "tweener" is often nothing more than chance.
However on the more general, or macro, level -- "pull the ball," "get it in the air," etc. batters can often exercise quite a bit of control and here's how:
Pitch type/location: A LH batter wanting to pull a ground ball can look for a pitch they are more likely to be able to pull on the ground, such as a pitch on the inner half of the plate or an offspeed pitch (that will cause them naturally to get the bat head out early). RH batters seeing a right-side hole can sit "fastball away" while in sac fly situations batters generally want to jump on pitches above the belt.
Quieter swing: Mark Ellis is a beautiful example of bat control. Several times this season, with a runner at 2B and nobody out, with two strikes on him and the goal just to make sure he advances the runner Ellis has very intentionally chopped a bouncer to the right side. He does it by quieting the movement in his swing (mostly just arms, less body), delaying bringing the bat head through the zone just a split second longer, and playing pepper with the right side of the diamond. This is a great "hit and run" technique, where an ordinary grounder has a good chance of becoming a "first-to-third single" even if it isn't hit especially hard.
Swing type: With two strikes, some hitters will choke up on the bat or shorten their swing, sacrificing power for contact and bat control, which increases the odds they can make solid (line drive) contact but brings the fences in 50 feet -- it basically turns hitters into Ryan Sweeney. It's no surprise that Jack Cust, whose swing is relatively big and long, has little bat control -- these guys are great to shift against because they cannot really adjust intentionally. In contrast, if Cliff Pennington or Gabe Gross were hitting into the Cust shift, they could easily find the gaping left side hole by waiting for a pitch away and putting a quick short "opposite field" swing on it.
There are many other categories and examples you can add, and I'd welcome you to add them in the comments. My main point is that while batters have little control over "a few feet here" or "looping liner to LF" vs. "slightly more arcing liner to left-center," as you zoom out to slightly more general parts of the field and types of balls hit, batters can exert quite a bit of control -- just as pitchers have weapons (sides of the plate, jamming swings, changing speeds) to combat these efforts. It creates a cat-and-mouse game of adjustments that is one of baseball's intricate joys.