Yes, I’ve seen what you describe, but I wouldn’t describe it as “underhanded”. I don’t expect to be credited to clients for solving problems. When I was heading up systems analysis at the bank, for example, if I had to call a customer to explain the resolution of a problem I didn’t personally solve, I didn’t say “Mr. Johnson, my employee Joe discovered that the error in interest was in an outdated ruleset regarding interest calculations on overdue promotional balances, and he passed it over to Amy, one of our coders, who flagged the ruleset and transferred your account information to me, at which point I corrected the ruleset, returned the interest charged back to your account, and gave you an additional credit.”
Instead, I’d say “Mr. Johnson, I apologize for the error [this, despite the fact that I didn’t personally cause it]; we corrected the interest charged to your account, and we’ve provided you with a $50 courtesy credit for the inconvenience.” Why? Because Mr. Johnson doesn’t give a shit who did what, and he probably doesn’t even care what the problem was in the first place; he only wants to know if and how it was solved. I know — as the manager presumably knows in your situation — who deserves credit for their work on the problem. My somewhat imprecise pronoun usage does not indicate that I think I should get credit for work I didn’t do.
Now, if you work in an industry where external recognition of your personal efforts affects you — commission-based sales, say, where you want the client to talk to YOU — then I retract my comments. If this is the case, though, why would the manager be talking to your client instead of you?