Yeah, I had experience with flooding in the basement when the washer's hose was leaking . It was a mess and I had to use a lot of towels and mop up the mess for sure. The other time in Utah, I lived in a basement apartment. The neighbor upstairs had a washing machine that broke and it leaked into our unit and flooded the place and the guys had to come over to clean up the mess and use a blower for a few days to dry the carpet and stuff. Also, in Seattle at a small 1 bedroom apt I lived in had a leak from the lobby that was leaking water from the fire sprinkler that failed, uh oh! So, that makes 3 times in my lifetime with minor flooding...nothing major. I hope you will be able to find a better place to live for sure. 
