Unfortunately, until humans have crypto modules installed in their brains, we will have to rely on some form of "security by obscurity" that many colloquially call "operational security".
Yes, there are types of data and metadata about your company's infrastructure that can be used against you. But no, you shouldn't hand it to attackers on a silver platter.
> In fact, to better test that this is the case, you should probably give the pentesters your account ID so you can be informed regarding your security in this scenario.
That depends on the scope of the test. Many organizations will do both (and others) to test different layers of security. Remote software exploits are something that many people on this forum are concerned about, but that is hardly the be-all-end-all of security for an organization. There's a lot of security topics entirely outside the scope of computer systems to be cognisant about here.