I don't know if J.B Rhine was specifically researching synchronicity. He was mainly researching mental telepathy. Having subject guess the symbols on these Zener cards. He then analyzed the results after many trials and did a statistical analysis of that to come up with the odds against chance. Out of the 5 cards, random chance would be 20% for a correct guess. I think this is where Jung saw the connection with synchronicity.
Most psychiatrist today believe that thing just happen randomly and there is no hidden meaning behind anything. Most think if you see special meaning in something, that is magical thinking and you need to be on medication.
There are a lot of book on Synchronicity now and a lot of people think there is something to it.
As far as questioning your beliefs when you mentioned working with a friend, here are 4 simple questions this author Byron Katie came up with.
I just copied this off Wikipedia. I don't know if you could use it or not, but I thought I would paste it in here.

Specifically. The Work is a way of identifying and questioning any stressful thought. It consists of four questions and a turnaround.

The four questions are:[8]

Is it true?
Can you absolutely know that it's true?
How do you react, what happens, when you believe that thought?
Who would you be without the thought?
The next step of The Work, the turnaround, is a way of experiencing the opposite of the believed thought. For example, the thought "My husband should listen to me," can be turned around to "I should listen to my husband," "I should listen to myself," and "My husband shouldn't listen to me."[8]

Then one finds specific examples of how each turnaround might be true.