FDR minimized exposure of his partial paralysis as much as possible but it was not a 'secret' that he had had polio. He held birthday balls which served as fundraisers for Warm Springs (a resort for polio treatment) and the polio foundation he created became The March of Dimes.
Woodrow Wilson, on the other hand, suffered from two strokes which left him completely incapacitated for quite some time. His wife, Edith, and a few close advisers, hid this and governed secretly in his stead.
I have no doubt that IF Trump was taken to Walter Reed for a health problem that they would lie about it. Nothing coming out of the WH or Trump can be taken at face value based on the innumerable lies they've told.