Tough question, and it can only be answered in a case by case way.

Some martial students are 'collectors' and treat forms, techniques and styles as if they are clothing, something to 'wear' to make themselves appear a certain way. They often have pictures of themselves 'posing' with a weapon or in a stance, but the picture won't be about the art, it will really be about how they 'look' doing it. This kind of student is NOT served by studying with multiple teachers, for he's just collecting and needs to learn to go deeper, not broader.

Some martial students are 'researchers' and seek knowlege as a means to deepen their understanding of what they know and where they are going. These students are helped by exposure to other methods/styles and a unthreatened sifu should let them go, since he'll get back a better person.

How to seperate the two? Only time and behavior are the indicators of which is which. A person's words are next to useless.