That's not true. Without swap, you already have the risk of thrashing. This is because Linux views all segments of code which your processes are running as clean and evictable from the cache, and therefore basically equivalent to swap, even when you have no swap. Under low-memory conditions, Linux will happily evict all clean pages, including the ones that the next process to be scheduled needs to execute from, causing thrashing. You can still get an unresponsive server under low memory conditions due to thrashing with no swap.
Setting swappiness to zero doesn't fix this. Disabling swap doesn't fix this. Disabling overcommit does fix this, but that might have unacceptable disadvantages if some of the processes you are running allocate much more RAM than they use. Installing earlyoom to prevent real low memory conditions does fix this, and is probably the best solution.
Setting swappiness to zero doesn't fix this. Disabling swap doesn't fix this. Disabling overcommit does fix this, but that might have unacceptable disadvantages if some of the processes you are running allocate much more RAM than they use. Installing earlyoom to prevent real low memory conditions does fix this, and is probably the best solution.