What is the authenticity of a man's prayer with shoes on at his workplace, along with his statement that there is a hadith which says, "The default is to pray with sandals"?

Praying in sandals is permissible if they are free from impurity. The Prophet, peace and blessings be upon him, prayed in his sandals. Gabriel informed him that there was filth on them, so he told his Companions to wipe them and pray in them if they found any dirt on them. It is preferable to avoid this if it leads to soiling the mosque's carpets.