I'll preface this by saying I think people killing animals for fun are dicks and should be having their heads examined, not out collecting trophy kills. I agree with you.
Now that said, if you ever watch 10 minutes of Nat'l Geographic or the nature channel, you'll see lions and all other predators sneak up on weaker prey all the time. They'll get as close to an animal as they can. And if a lion had thumbs and fingers, they'd use a gun if they could too.
Humans in general have NEVER taken a knife and walked up to a lion single handed unless they had a death wish. Man has always hunted in packs and would hunt from a distance as often as they could. Spears, slings, bows and arrows, etc. are all part of the weapons arsenal of hunting parties from the past. Archeology tells us this.
The issue has nothing to do with using a gun, it has to do with the trophy kill.