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Would you send an oracle guy to deal with a corrupted SQL server install, or possibly worse still vice versa. In some ways they might be worse choice than your cisco guy, at least he definitely knows he doesn't know anything about it...
You could send either of your dba's to figure out why something was slow though, they might end up calling out the network chap, if it was client to server...
The fundamental any generalist or specialist in anything needs to have troubleshooting, and that's so far from a given it's not true.
The thing is if a client has problem where there are a number of possible areas where something could be wrong, sending an expert in one of them is troubleshooting failure number 1, you just guessed where the issue was and worse still by sending your expert in X, he's going to assume it is X that's at fault. If they aren't a good fault finder, they'll be shaking the machine to dislodge the gremlins instead of making sure the printer is turned on....

The assumption you are talking about is one prevalent right across IT amongst the non-technical, it's why people come up to me as programmer and ask me to sort out an active directory problem, or a PBX, or fix their scanner...

The above is the first thing a generalist should know, and it's a good generalist you should send first so then they can call in the correct specialist.

So as usual it would seem you've got it bass ackwards again, you should be making sure your specialists have the fundamentals, or employ some fundamentalists.