The specific agreement entered into on Nov. 6, 1861 between Missouri Governor Gamble and President Lincoln was that the MSM was authorized to act outside of Missouri "in the immediate defense of the state." That's an incredibly broad imprimatur--worded, I suspect, to quell anxieties of rank and file MSM troops and the Missouri populace, while at the same time providing the Federal powers that be the ability to do pretty much as they pleased with the force as long as a threat to Missouri was asserted. With that wording, the MSM could have been sent to Texas, or Mississippi, or even Florida, if it was claimed that Confederate forces were being marshaled there that were going to target Missouri. Any MSM troops deployed in such a manner probably would have objected, but the legal basis for utilizing them as outlined existed.

Regarding this huge loophole, remember that Lincoln was considered by many to be one of the great legal minds of his day, while Gamble was a former chief justice of the Missouri Supreme Court. And it is very likely that Governor Gamble's brother-in-law, Edward Bates--another preeminent legal mind of the day and who was also from Missouri--had a hand in crafting the MSM authorization in his dual role as United States Attorney General and President Lincoln's chief legal advisor (actually Bates was probably the primary architect of the agreement that created the MSM).