The 'tail between the legs' is going to played up by the media and other conference members but I do not see it that way at all.
Texas A&M is doing exactly the right the thing by looking for an 'exit' strategy from the Big 12. No program is hurt more in the Big 12 than A&M. Texas has benefited 1000% from running the Big 12 and keeping A&M under wraps.
Step back into the time-machine during the end of the SWC and the formation of the Big 12. Despite UT's overall prestige A&M was the power program continually in the Top 5 and Texas was a 6-8 win team with coaches like John Mackovic. That has completely flipped in every aspect and will never change as long as A&M is tied to Texas.
Going to the SEC(best choice) or even the Big Ten(to a lesser extent) removes the shackles and allows A&M to offer a recruiting advantage/differentiation from Texas. Does it make A&M the new Texas no, but it certainly offers real competition for the first time.
Understanding this is how Texas despite their public comments is concerned about A&M to the SEC. Not only does it put A&M in the best football conference but it creates competition for Texas recruits and opens the door for the SEC into Texas. All of this means over time Texas will not get the defacto pick of the first 20 best players year in and year out -> the margin for error tigthens and that means more losing. Can be the difference between winning another national title.
Not saying this is going to happen... but ..... if I was the key Big Ten decision maker I would accpet an application from A&M in a heartbeat. It does mean more travel, etc. but it allows the Big Ten to get into a southern, massive market. A&M is good accademically also which fits into the Big Ten model. From A&M's inclusion in the Big Ten would provide stability but not be an ideal choice as travel is increased, no natural border rivals and cold weather..... but they must get out from Texas to thrive.