I totally agree on that Howard Aiken quote, but the type of people who run YC and those that apply to and get into YC aren't the type of people Mr. Aiken is talking about.
I tell everyone loudly about what I'm working on and other ideas I've had, but I'm not working on, and I've noticed that those that have the foresight to get understand of them and their value more closely approximate the types of people that get into YC.
Assuming that my point is true and that my ideas and some of the ideas of YC applicants are good, then in applying to YC, we are subject to the issue you state in the first line.
"I also tend to fear that my ideas might be stolen, but the truth is that anyone who is good enough to make something work generally has too many ideas on their plate to steal someone else's."
The problem now is that there are people who are going into YC not with too many ideas, but one they are working on, but with no ideas.
I would say that there is certainly a conflict of interest, not a huge one, but one nonetheless. That being said I think it's still worth applying, because there's a lot more details in an idea than fit in a YC application. Oftentimes there are months to a year or more of thought in a YC app that an idea-less team won't have the luxury of having if one of the YC partners suggests the idea/market to that team, even if done so subconsciously and without malice (i.e. not citing the specific application, or even remembering having read it.)