From an Islamic perspective, the important thing to remember is that everything happens in the universe through the permission and power of Allah. The universe is in constant connection with Allah, and Allah is the provider and the sustainer.
In the modern era, a model of the universe that is essentially impersonal and material has taken root. As a result, some Muslims see Allah as only the original creator who started up the universe (the "clockwork universe") but then left it to run by itself only through material means. Therefore, they find it very surprising if anything ever happens - such as an answered prayer or a miracle - that does not have an obvious material cause or should not have happened ordinarily.
In virtually every culture around the world, Muslim and otherwise, before the rise of scientific modernity, it was generally accepted that things happen also through non-material means, and also that human beings have the capability to influence the universe around them through non-material means. (For instance, prayer, or giving someone the evil eye) For most people, this capability is more or less latent, but the Qur'an gives examples of those who had a tremendous capability to influence the universe, such as Jesus (A). Many Shi'is also believe that the Prophet (S) and Imams (A) had authority over creation (wilayah takwiniyyah).
However, the important thing to remember in this worldview - as mentioned above - is that Jesus (A) was not influencing an impersonal, secular, wholly materialistic universe; rather, Jesus (A) is influencing the universe to manifest reality differently through the power of the divine.
Some people who promote this sort of belief do so with a model of a wholly secular, materialistic, and non-meaningful universe, and this is not accurate from the viewpoint of Islamic theology.
Certainly, all human beings can manifest positive thoughts (through the will of Allah) through prayer, and there are different types of prayer. Meditating on a positive thought is a form of prayer, although it lacks the religious overtone of praying to Allah as a servant of Allah, as is recommended in Islamic texts. Still, there is no reason why the creator of the cosmos should ignore a prayer just because it is expressed in a different manner. Do not our du'as say that Allah answers the prayers of those who know Him and also those who do not know Him? Certainly, fish do not pray in the same way that humans do but also enjoy divine sustenance and protection. It is also narrated that Allah is shy to disappoint the believer who has a good opinion of Him. As human beings, we tend to have a very limited perspective on what Allah is or isn't, or what Allah would respond to.
This is apart from the wholly psychological and self-fulfilling aspect of such things; that is, when we expect to succeed, we often will; and we expect to fail, we often will. Generally, it is healthy to have a positive (although realistic) attitude and for the believer to be optimistic.
Beyond that, ideas such as this can be tested in practice and one can see personally whether they are true or false. In fact, even whether or not prayer is effective can be empirically tested!
That being said, sometimes things like this are discussed in a rather fluffy sort of manner, so it is worthwhile to take things that people write or say about it with a grain of salt and sift out the things that are silliness or just speculation.