Did Edith Give TR $20 a Day?

There's a story floating around that Edith gave TR an allowance of $20 a day. It showed up in an October 30th, 1932 article that appeared in the New York Herald Tribune written by Edith’s personal Secretary Isabella “Belle” Hagner.
Belle wrote TR met a friend at a bookstore who wanted to buy a book, but only had 25 cents in his pocket. She said, TR laughed and remarked Edith gave him $20 every morning and by the end of the day he didn't know where it went. In Sylvia Jukes Morris's biography Edith Kermit Roosevelt - Portrait of a First Lady, she brings up the same story and sites Hagner as the source.
Is a fun story, but loaded with problems. To put things in perspective, based on the Bureau of Labor Statistics Consumer Price Index, $20 in 1902 is equal to $753 a day in 2026, or the equivalent of $274,845 a year. That's some allowance. Today that's like $5,285 a week in pocket change.
Here's what TR could have bought every day with $20 back in 1902. Five tons of coal, 1,400 lbs. of potatoes, a refrigerator, enough chicken breast to feed 70 people, 80 tickets to a Broadway show., a cow., a stove, a washing machine, a sewing machine or a large 1,500 lbs. solid steel concrete filled fire resistant safe.
If Theodore Roosevelt could spend $20 a day in 1902 and not know where the money went, how did he get up on Mr. Rushmore?
