Yes, it's true. You can check the multipliers by clicking on any name @ https://splintertrends.com/leaderboard. E.g., @h4rr1s s buys a token every month:

The only thing that can break your loyalty multiplier is if you sell your tokens or create a sell order. The order in this case is LIFO; the last obtained tokens lose their multipliers first.

I know it's complex, but there is logic in it 😉