All the banks deal with and depend on each other. Also, in a bubble most banks are invested in the same scheme. When the bubble finally pops, all the banks get in trouble. So "financial system" is exactly the right term.
There are alot of banks and even Hedgefonds that did not invest into realestate (because the could not actully figure out what that stuff was worth and didn't buy them just because it was what "The cool kids where doing") and where not in trouble. An yes you are right the hole system has "trouble" but the system wont just crash. Everybody that is "bad" will go done and maybe some others will go down but if a bank had enough reservse and had not a shitlode of bad asseds the could survive the storm. The remaining good asseds of the banks that go bust will be liquidateted. The conservative banks can now make the money that the did not get in the boom years.