What version, and what OS? I've never encountered such a request.
(The mention of 'key chain' suggests a recent Mac OS, because that's qhere all your passwords are stored. However, I don't think Abode ought to have anything to do with this.)
MAC OS 10.5.8
Jack: I think you're overblowing this.
When there is a crash, InDesign's crash reporter normally pops up, and gives you the option to submit the crash information to Adobe.
This is important to do, because Adobe tracks why the program is crashing and puts engineering effort into fixing the most frequently occuring crashes. Everyone should always submit every crash report, with appropriate narrative.
In order to submit the crash report, the crash reporter program opens an Adobe web page using https, the secure sockets protocol (SSL).
In order to do so, it needs to verify the SSL certificate associated with the Adobe web site, just as any other web browser does when accessing any SSL-protected (https) web page.
Your machine is set up such that programs that try to access the certificate repository need your explicit permission to do so, and that is what is going on with the message you see (this may be related to your proxy server as well).
Additionally, the crash reporter can also be configured to Always Send Crash Reports (without prompting the user), or the Never Send Crash reports. If you're not seeing the crash reporter pop up (and you haven't described it), then it sounds like the first has been set. This is not a setting Adobe ships with -- you or your site administrator would have had to configure it.
Coupled with your firewall/proxy/certificate/SSL settings, it is certainly odd. But not, I think, cause for concern.
Anyhow, you can adjust this setting by opening /Applications/Adobe InDesign CS5/, rightclicking on the .app, going inside the package, and navigating to Contents/Frameworks/AdobeCrashReporter.framework/Resources/ and running Adobe Crash Reporter.app.
You will get a dialog box allowing you to choose between the three settings.
But again, please don't choose Never Send -- it deprives Adobe of critical information to make the product better for us all.