The statement is false because even if a server has sufficient swap space, it can still encounter Out of Memory conditions. Swap space acts as an overflow for when the physical memory (RAM) is fully utilized, and it allows the system to continue running by temporarily moving some memory pages to disk. However, swap space is significantly slower than RAM, and if the system is under heavy memory pressure, where even the swap space is entirely used, it may still trigger the OOM killer to terminate processes to free up memory. Additionally, certain situations, such as kernel memory allocation requests that cannot be swapped out, may also lead to OOM conditions regardless of the available swap.