The story is possible, but more likely seems to be an embellishment of an otherwise true story.
From the Stanford University website...
The story goes that in 1892, Herbert Hoover, a member of Stanford's Pioneer Class, invited Polish composer Ignacy Jan Paderewski, one of the leading pianists in the world, to give a benefit concert. Due to problems with scheduling and publicity, only a few people attended. Hoover asked the pianist not to play, but he performed anyway, waiving his concert fee. And when Paderewski discovered that Hoover owed thousands of dollars for rental of the concert hall, the musician covered the bill. That incident marked the beginning of a friendship between the two men that would last 50 years.
During and after World War I, when Poles faced massive starvation, Hoover repaid his debt to Paderewski, who became Poland's prime minister, by organizing the largest relief operation ever mounted in Europe, said Zbigniew Stanczyk, East European specialist at the Hoover Institution.
The following are confirmed true aspects of the story.
Mr. Hoover and Mr. Paderewski met at Stanford in 1892 under the pretext of a concert.
Mr. Hoover had difficulty in coming up with all of the funds in order to pay for the concert after scheduling conflicts.
Mr. Paderewski covered the bill upon discovering this
The friendship that resulted from this meeting was a factor in delivering foreign Aid to Poland after World War 1
What is unclear.
- What the "benefit concert" was benefiting. It is conceivable that the benefit concert was for the purposes of raising tuition funds.
The earliest reference to the concert being for the purposes of tuition I could find online was from this bible.org page, which in turn references the book "Perhaps I am" by Edward Bok.
There were once two young men working their way through Leland Stanford University. Their funds got desperately low, and the idea came to one of them to engage Paderewski for a piano recital and devote the profits to their board and tuition. The great pianist’s manager asked for a guarantee of two thousand dollars. The students, undaunted, proceeded to stage the concert. They worked hard, only to find that the concert had raised only sixteen hundred dollars. After the concert, the students sought the great artist and told him of their efforts and results. They gave him the entire sixteen hundred dollars, and accompanied it with a promissory note for four hundred dollars, explaining that they would earn the amount at the earliest possible moment and send the money to him.
“No,” replied Paderewski, “that won’t do.” Then tearing the note to shreds, he returned the money and said to them: “Now, take out of this sixteen hundred dollars all of your expenses, and keep for each of you 10 percent of the balance for your work, and let me have the rest.” The years rolled by—years of fortune and destiny. Paderewski had become premier of Poland. The devastating war came, and Paderewski was striving with might and main to feed the starving thousands of his beloved Poland. There was only one man in the world who could help Paderewski and his people. Thousands of tons of food began to come into Poland for distribution by the Polish premier. After the starving people were fed, Paderewski journeyed to Paris to thank Herbert Hoover for the relief sent him.
“That’s all right, Mr. Paderewski,” was Mr. Hoover’s reply. “Besides, you don’t remember it, but you helped me once when I was a student at college and I was in a hole.”
However, the book itself is not quoted directly and there are not any sources online that could be used to prove or disprove that the book is even properly cited.