This is exactly what the manual says:
Recommended Fuel (6.2L
V8 Engine)
Premium unleaded gasoline
meeting ASTM specification D4814
with a posted octane rating of 93 —
(R+M)/2 — is highly recommended
for best performance and fuel
economy. Unleaded gasoline with
an octane rated as low as 87 can be
used. Using unleaded gasoline
rated below 93 octane, however, will
lead to reduced acceleration and
fuel economy. If knocking occurs,
use a gasoline rated at 93 octane
as soon as possible, otherwise, the
engine could be damaged. If heavy
knocking is heard when using
gasoline with a 93 octane rating, the
engine needs service.
Nothing is said about a warranty claim being denied by using 87 octane. Obviously performance will not be as good as using 93 octane but if you are not putting a heavy load on the engine and there isn't any knocking I don't see what the problem is. BTW - my C7 says the same thing about the 6.2L in it. I does say to use at least 91 octane in the supercharged version.