It does happen...President Lincoln provoked the Civil War by supplying Fort Sumter, I believe it was, on Confederate territory. The Confederates took the bait, and Lincoln could tell the half-truth by claiming "They started it."

Also happened when America was trying to take over all of Texas as it is today. America said the Texas Border extended past the (San Juan?) River, Mexico said it didn't, we built a base on (San Juan?) River, and wah-lah. Flawless.