The law does not say that. The law only says that Confederate veterans (of which there were in 1958, wait, let me check, zero) will receive the same pension as United States veterans.
We must be reading a different law, or perhaps you believe dead veterans are no longer veterans. Let me post the changes to the law, in context, so the readers will know what we are referencing:
"AN ACT: To increase the monthly rates of pension payable to widows and former widows of deceased veterans of the Spanish-American War, Civil War, Indian War, and Mexican War, and provide pensions to widows of veterans who served in the military or naval forces of the Confederate States of America during the Civil War."
"Be it enacted By the Senate and House of Representatives of the United States of America in Congress assembled, That the Veterans' Benefits Act of 1957 (Public Law 85-56) is amended:"
"(3)(e) For the purpose of this section, and section 433, the term 'veteran' includes a person who served in the military or naval forces of the Confederate States of America during the Civil War, and the term 'active, military or naval service' includes active service in such forces."
[Public Law 85-425, in "U.S. Code on Confederate War Veterans." 1958]
I interpret that law to define a U.S. military or naval veteran to include those who actively served in the Confederate military or naval services. Perhaps you were unintentionally misdirected by the terms "pension" and "widow."
Mr. Kalamata