As an atheist I attempt to also remain a latitudinarian as well, in the modern sense of the word, therefore please permit this commentary with that in mind. Although my experience in life as reflected in the time spent treading this Earth is by no means as great as many of my peers, I too have experienced such unusual connections between people in my travels. However I propose that before seeing a hand of divinity or some greater force at work, the simple elements of random chance and favorable memory must be factored into any considerations of the day's events. First the unusual moments as one is out walking, buying an item in a store, or otherwise involved can leave a powerful impression if they happen to fall on fertile mental soil. For example if one is having a difficult day and the person manning the counter at a coffee bar, for no apparent reason, suddenly states your drink is on the house because you are having a difficult day it can appear profound. More concrete examples can of course involve detailed information, a moving statement out of nowhere or a gift at the right moment.
At the same time though it is necessary to weigh any feelings of divine intervention against all the other encounters that one has during the day that are similar but do not have the same feeling. The gentleman trying to make small talk with you while you wait for the bus, the odd individual who out of the blue asks if you have worshipped the small chipmunks that day. In my own personal experience riding the bus each Thursday for class I shared the bus with a lady who spent the entire trip explaining to everyone how she was an emissary for Christ and was spreading his word. I equate her in this same category of untimely messengers because not only did her statements gain no attention from other passengers or myself but she also preached a version of the gospel that I personally doubt is commonly accepted. Her focus was more on how Christ could blow down cities with one breath and his foot was literally mighty enough to crush mountains. But I digress, these examples are useful because they illustrate during our day we have various contacts that are unusual, as to if they are profound or merely abnormal, I contend that has more to do with the participant then any outlying cosmic design.
I only state this in an effort to encourage people when considering such events and attributing them to divine design to be cautious in the application of that label. Before making such a statement consider the basic human desire to seek patterns amid the normal flow of chaos, to seek some overlying order to the apparent lack of pattern present in our world. Although I am no expert in all that is humanity, nor could I ever lay claim to such a title, at least in my case it is the overuse of the divine as an explanation weakened my early faith in the divine. My eventual realization that I lacked faith, i.e. I was an atheist, came for many reasons but the commonality of divinity was one element in that realization. However even with that consideration in mind should one still feel the hand of a divinity or the guiding current of a cosmic order greater then humanity, by all means attach the title.
I only write this as a reminder that when considering the profound do not do so at the expense of the mundane. On an interesting side note if one is interested in god and the use of sock puppets, I recommend examining the online comic Sinfest, which has several panels dealing with this idea in a humorous, albeit literal, manner.