With the Walker pick, I remember the Spurs at the time said that Lonnie was by far the best prospect on their board at their pick, and they took him without hesitation since he was rumored to go in the lottery before his knee injury close to the draft. With regards to the Luka pick, it's the most debatable one of the three I'd guess (and posters here will never shut up about it, unless Luka makes an All-Star team or something), but a post-draft writeup by timvp indicates the Spurs strongly liked Sammich and didn't think he'd be there at 29. With Vassell, he was rumored to be Boston-bound if he dropped to #14, so there wasn't a lot of margin for negotiation if the Spurs wanted to draft Devin (and even then, they ran out the clock on draft day, presumably on the phone with other teams).
There just isn't much room to maneuver if you're certain that you want a specific prospect. Cases like Tatum's drafting, where Boston was able to both trade down AND get their guy, are the exception and not the rule - and the fact that, in basketball, a dime can be worth much, much more than two nickels also contribute to this.