Yes that is true and you are correct if I may say, I have experience similar things before. Not directly jumping around in comparison of odds but rather it's entirely for luck as one could be that lucky enough to have the beginners luck while trying out from other casinos. Then, there was this casino I usually have luck to win on their gambling site before they ceased their promotion here.
When gambling, trying out other sites is not completely a crime but the gamblers choice if I may know.
It's like very attractive factor on user decision making but beyond that, they need to take a general reputation of a gambling site into consideration. If its reputation is good, it's more guaranteed that the gambler will be paid fairly and fully if he wins bets on that casino. This principle is applicable with all casinos, and all bet products and not limited to sport bets.
Because whatever the odds is good, if in the end, the casino refuse paying money to the gambler, that sucks for the gambler as their wins mean nothing in the end.