Who Refers Work to a Competitor?

I took a call from a client. They asked for something that we can do but don’t do particularly well. I decided to refer the project to another shop that does that one thing very well. The other shop also has some competitive overlap with us. What am I thinking?
To compete or to collaborate? Beyond that and a seemingly crazier question: to block work from competitors or refer it to them? I’ve prioritized getting to know as many people in our business as I possibly can in the Houston market. I often have coffee with direct competitors. I often share ideas and work with people that could easily replicate it and take credit. It’s quite possible that I’m too young and naive to realize the risk I’m taking on…I acknowledge that.
However, I can’t help but feel like the creative community in a city like Houston (not typically known for its creative brilliance) is strengthened by the collaboration of competitors. Sure, we have to survive and protect our client relationships. But in the interest of authenticity, efficiency and quality, don’t we do our clients a disservice by attempting to do work we know we’re not very good at instead of referring it to someone else that does it very well? Will the client view that as an act of good faith and honesty? Or will the client walk right on through the open door you’ve just presented to them and leave you standing in the cold? Either one is possible, and if you do this long enough, both will probably happen at some point.
So let’s look at this from the perspective of the Marketing Director and the perspective of the agency.
I’m confident in saying that you’ll get burned far more if you’re the cut-throat business owner that will tell your client anything to win more business and disrespect your competition. Sure, both approaches have worked in the past. But we’re also not currently living in the past. Cut-throat competitive and management strategy isn’t going anywhere, but it’s success rate sure is. Treat people well. Your employees, your clients and yes, even your competition.
What do you think? The words of a naive “kid” in the business who needs a few more rodeos under his belt?