I don't think there's anything wrong with trying out different approaches. However, I wouldn't be too concerned about a teacher saying to his or her students 'concentrate on x - don't worry about y'. For the vast majority of us, as householders, we don't have the time or the personal resources to engage in practicing all the various samatha techniques uninterrupted for years on end in total seclusion, nor the time to practice all vipassana variants.
At some point, I believe, one must devote oneself to one particular approach for a length of time to see if it gives benefit. If it doesn't one simply moves on. But having a teacher (let's say another hypothetical teacher), who provided his students with a variety of practices could be counter to the student making any progress at all. One does a little bit of anapana, earth kasina, perhaps vipassana, contemplation of death and others. One may not get established in either one and there is a danger that such approach can turn the experience into another sensory entertainment, a smorgasbord.
It was the students of Webu Sayadaw who said that he became an arahant on little more than observing his breath. On reading his discourses, it is clear that he knew nothing of the Abhidhamma and according to U Ba Khin and others, the Sayadaw knew no Pali.
So I don't think its a problem. If one doesn't get benefit from one's teacher's approach following a trial period of following that teacher's instructions, then move on.
“No lists of things to be done. The day providential to itself. The hour. There is no later. This is later. All things of grace and beauty such that one holds them to one's heart have a common provenance in pain. Their birth in grief and ashes.”
- Cormac McCarthy, The Road
Learn this from the waters:
in mountain clefts and chasms,
loud gush the streamlets,
but great rivers flow silently.
- Sutta Nipata 3.725
(Buddhist aid in Myanmar) • •