True or false?
The statement is false for two reasons. First, the words welfare optimum are imprecise and misleading. Economists can talk about efficient, Pareto-Efficient or Pareto-Optimal outcomes---meaning that the mix of goods consumed and produced in the economy is one for which no adjustment could make anyone better off without making someone else worse off. But this does not mean that the distribution of income is a good one, and distribution considerations must also enter into any statement about welfare. Second, perfect competition will lead to a Pareto-Optimal situation only if there are no externalities---this is the First Theorem on Welfare Economics.
If transactions costs are zero and property rights are well defined, a Pareto-Optimal situation will result even if there are externalities and even if there is not perfect competition. If anyone can gain by a particular adjustment after compensating the losers to keep them as well off as before, the gainers will bribe the losers and Pareto-Efficiency will be achieved. This is the Coase Theorem.