This is a great policy. Sometimes a follow up at just the right time can really help too. Always be respectful, after all it's the client's choice, and be understanding that they are going to feel a bit embarrassed when the first results come back from the cheap place. Have a supporting story that lets them save face "I can see you're really a cost conscious guy, that usually correlates with a good sense of value too, while my stuff is a bit more expensive let me share with you what we do to make sure you will be satisfied ..."
The problem is that these clients have a particular budget. Perhaps they have $15,000 to spend. I tell them it's going to be $18,000. Someone else tells them they can do it for $7,000.
They go off and spend $7,000, then come to me because it wasn't done properly and say, "Unfortunately, it really didn't work out with these other guys - can you please, please help me out?" Now the problem is that they only have $8,000. Where before I might have been able to cut scope a bit to get down to $15,000; or perhaps they could have scrounged up another $3,000, they are now completely out of luck. And it sucks to see this happen to people.
On the other hand, sometimes people who charge less do a great job. As much as I'm not the cheapest person around, I'm also not nearly the most expensive, and I still do good work. To someone at the high-end, perhaps I'm one of those low-cost, risky alternatives, although I don't see it that way. The problem for the average client, though, is they generally lack the experience and understanding they need to properly evaluate all of their options.