I believe that you are wrong. If there is a large trend of low multipliets, then the next bets are more likely to be higher because although the 2 games are independent the chance of losing grows less. Think of a coin. The chance to get 2 tails in a row is (1/2 * 1/2) or 1/4. There is a similar effect at bustabit. So yes, I believe that the rounds are linked. You can't predict it, but you can get a greater chance at winning.
With a fair coin, the chance to get 2 tails in a row is 1/4. Yet, given that the first flip is a tail, the chance to get 2 tails in a row is actually 1/2, exactly the same as the chance to get a head in the second flip. The simple example on
https://en.wikipedia.org/wiki/Conditional_probability#Example may help you understand the concept of conditional probability.