No it is not true. Most rabbits have no issues with proper wire floors, depending on the environment etc. those can have quitw some advantages. Very big breeds and Rex furred rabbits can have have problems though. There is agood reason many breeders in the US use them, they wouldn't if they would cause issues.
Wire has a bad reputation, here it's imho mostly due the decades long fight to free chicken wire cages. That got pretty uncritically gerneralized, without good arguments, anything wire equals evil.
Anyway, I don't use cages, whatever available would be way too small for my taste, and in our climate wooden hutches are better (mine have wood slat floors), and my two house rabbits don't have any enclosure, just need to stay inside during night.