Maybe not the button push but you might be able to with your composition and timing (although not usually to the same degree as a a painter would).
I agree, Matt, but the timing thing applies especially to street photography. That's where Slobodan jumps the track.
With landscape you go out in wretched weather and set up your tripod; hoist your 11 x 14 view camera onto it and try to get it pinned down without dropping it on the rocks and smashing the ground glass. You attach your cable release, get your head under the hood and zoom the bellows back and forth until you think you've nailed the focus, pull a film holder out of the case you've carried over the rocks on your back, shove it into the camera, and wait for the "decisive moment," otherwise known as when the sun pops out. When that moment arrives you pull the slide on the film holder and "push the button," otherwise known as the knob on the cable release. Then you push the slide back into the film holder, hoping to hell you got the shot because the sun just disappeared again, pack up your gear and walk two miles back to the car.
On the street (HCB) you have a small, 35mm or equivalent camera in your hand. You go about your business, nosing into various establishments and turning corners, until you see what looks like an interesting situation developing. You grip the camera and wait, holding your breath and hoping what you thought would come together will come together. If it does, you quickly lift the camera, watch for the "decisive moment," which is the moment when YOU decide it's time to shoot, and shoot.
In the first instance, whatever there is of you in the picture was there when you framed the thing and busted your butt getting all that equipment into place. The button push is nothing. In the second instance what you put into the picture was your choice of the instant you chose to push the button on a very transient scene. It's a different kind of thing. In the first case those rocks looked the same fifty years ago when St. Ansel shot then as they looked this morning when you shot them, and they'll still look the same fifty years from now when the next would be St. Ansel comes along to shoot them. In the second case the people in the picture you shot -- along with you -- probably will be dead.