In my experience, it is situational.
If the deal is locked up, meaning an integrator who has a lot of history with the manufacturer is managing the deal, any sales person who tries to get another integrator involved in probably going to get a stern reprimand (unlikely to get fired for a 1st or 2nd offense). There is very little upside to messing with variables in an all-but-won opportunity. But, this would be a weird and strange situation, and an indicator that the sales person is maybe not that bright.
A more likely scenario is that the deal is being managed by an integrator that the sales person/manufacturer has less confidence in. Maybe this integrator is known for being overpriced on labor, or trying to cheap out and selecting the wrong components which potentially leads to an unsatisfied end user. In that case, I have seen RSMs/RSDs steer a deal to a different integrator to give it a greater probably of closing in the manufacturers favor.
Despite what some people like the think, I have found that manufacturer sales people are, for the most part, decent people who don't want to introduce any more drama than is necessary. However, these people are measured, and paid, on what they close, and they WILL act in their own best interest to get a deal done. If they feel a given integrator can not close an opportunity for some reason, they are likely to try and bring in a different integrator to "save" the deal (and their own commission). There is somewhat of an art to being able to discern when and how this needs to be done so that you can maintain relationships across the board.