One theory widely aired on social media - and by some political opponents - was that Buhari had been replaced by a lookalike from Sudan called Jubril.
The country's president called the incident a "national disaster."
Many people are already comparing him to GOP nominee Donald Trump.
The girls have been held hostage for more than two years.
Martha was suddenly awakened by what had become the all-too-familiar sound of gunshots. Boko Haram, she thought. As she scurried to gather her thoughts, her husband Mark was already rushing their younger, panic-stricken children out of their home in Chibok, Nigeria.
As the hours, days, months, and years drag on, Mary clings to the hope that her missing daughter will be found. Last September
President Muhammadu Buhari, elected last year largely on his vow to fight corruption, has vowed to recover "mind-boggling" sums of money stolen from the oil sector.
Two years on, and their parents still wake up each morning not knowing whether their daughters are alive or dead, married or single or violated as slaves. They surely deserve more than a forlorn hope. The girls are now a symbol of our apparent weakness to protect young lives.
"I write this letter with a heavy heart, knowing you have endured another year separated from your daughters."