Well, thats what Richard at BJ told me. I have not researched the species myself, so I was going on what he told me.
I just read up on the species and it is found in dry prairies of the Chaco of Argentina, Brazil, Bolivia and Paraguay. So maybe when talking to Richard, my brain clicked onto desert.
I went to the IUCN web site and they list the following habitats for Phyllomedusa sauvaggii.
List of Habitats:
1 Forest
1.5 Forest - Subtropical/Tropical Dry
2 Savanna
2.1 Savanna - Dry
2.2 Savanna - Moist
3 Shrubland
3.5 Shrubland - Subtropical/Tropical Dry
3.6 Shrubland - Subtropical/Tropical Moist
3.7 Shrubland - Subtropical/Tropical High Altitude
5 Wetlands (inland)
5.6 Wetlands (inland) - Seasonal/Intermittent Freshwater Lakes (over 8ha)
5.8 Wetlands (inland) - Seasonal/Intermittent Freshwater Marshes/Pools (under 8ha)