Yeaaahh... I think the point being made is you would have experienced that regardless to who, or what, you were praying to and... quite possibly if you weren't praying at all. People all over the world have experienced the same sort of things, both in and not in the presence of religious (or otherwise) prayer. One of those correlation =/= causation things. Hell, as a minor personal example, simple meditation (which, functionally, religious prayer is just a methodology thereof) did a tremendous amount to help me psychologically when I was younger, and to this day I often use a simple (and, frankly, mangled) buddhist mantra (that I can no longer even recall what is supposed to mean) to help focus and work through rough spots. It's often not the meaning that's important, but the method.
Reason it's actually worrying to some people is because, beyond the conceptual or theoretical aspects of it, a strong emphasis on prayer... gets people killed. Regularly. Because folks will trust prayer more than actual action... turn to faith healing instead of a doctor, and whatnot. And for every one that does that and sees results... many,
many more
don't. I'd be the first person to express approval for meditative practices -- including prayer -- but also the among first to warn against attributing more to the practice than is appropriate, yeah.
I guess the half-point is that you're very welcome to express your belief in the practice, just... expect people to also express their concerns, y'know?
As the aside, I've always been fond of the conceptualization of prayer as a thing expressed through action, instead of words -- that you express your love for and belief in the divine through good works instead of a bowed head and mumbled benedictions. From the christian perspective, one could say that when one
walks with Christ, every step is a benediction to the glory of the lord, every hand extended in mercy a hymnal to the righteous path. To
speak of christ is to of very little... weight, y'know? Comparatively. Kind words are a lesser thing than a kind shoulder to lean on. Occasionally all there is to be done is offer words, but... in that case, instead of offering words to the sky, offer an arm to those near -- better the world around you when you cannot better the world afar. Through that is message of rightfulness made manifest...
... I haven't actually seen that sort of thing very often on the ground, though