During and after the war, many in the United States placed the majority of the blame for the Mexican-American War squarely on the shoulders of Mexico. There may be a grain of truth in this ultra-patriotic view (Combs 99). President Polk sent troops under General Zachary Taylor to the region between the Rio Grande and Nueces Rivers. Texas believed that its southern boundary was represented by the Rio Grande River. The Mexicans, however, did not acknowledge this boundary and instead believed that it was the Nueces River. So, the Americans believed they were on Texan (soon to be American) soil, while the Mexicans believed that the Americans were on Mexican soil (Lavender 130). When Mexican forces attacked the Americans in this region, Polk believed that Mexico "invaded our territory, and shed American blood upon the American soil" (Richardson 442). With this information in hand, Polk proceeded to ask the Congress for a declaration of war, which he received easily. However, according to Polk's diary and other sources, he planned to ask Congress for a declaration before word of the Mexican "attack" ever reached Washington (Quaife 386). Refuting this "Mexico's Fault" theory even more is the fact that the government of Mexico at this time was in a period of chaos (Garraty and Gay 811). Still, the attack proved an effective scapegoat for not only Polk, but many other pro-war politicians.
That foreign nations recognized the Rio Grande, is irrelevant to what Mexico believed.
http://www.azteca.net/aztec/war/Mexican-American-War.html
It would seem to me that you are mistaken. Santa Ana agreed to it per the Treaty of Velasco, which also had a provision requiring him to withdraw all Mexican troops to his side of the Rio Grande. Of course the Mexicans reneged on this almost immediately and renewed their efforts to reconquer Texas, but by that time Texas had already been welcomed into the community of nations whether Mexico liked it or not.
It is also false that the Mexicans acknowledged the Nueces River as their boundary with Texas. In fact they never even recognized Texas at all! In 1845 they still considered it a renegade province and were still trying to retake it. The Nueces River claim was nothing more than an arbitrary piece of specious nonsense they threw out after annexation in hopes of regaining the southern part of Texas since they knew they couldn't go up against the U.S. army. Thankfully General Taylor wasn't interested in playing their games.