Your friend MAY be right, but it really just kind of depends on if the adapter is defective or not. Every time you have some kind of an adapter or converter, some part of the signal is going to be lost, that's just unavoidable. Now 99.9999999999999999999999% of us are not aurally sensitive enough, and/or just don't care that much, about the rather minute amount of signal loss.
Of course the other risk you take with these adapters, is that there's one more link in the chain to break, and one more thing you have to try and isolate and test when things go wrong. So I'm of the KISS mentality on this sort of thing. The fewer adapters the better. If you absolutely need one for some reason or another... Fine, but they should be kept to a minimum.
But why do you need iTunes to be messing with the EQ when you've got a home theater receiver that has a full fledged DSP chip that will likely do a far better job than iTunes could ever hope to? That might even be part of your problem, is that the receiver is expecting the output to be the nominal signal, no post-processing, then it does it's own post-processing, and things don't go so well.
Whatever the case, screw iTunes' EQ, let your receiver work its magic. The resulting audio will likely be considerably better. And if you can do optical to and from, as you apparently can, even better, because then you have less signal loss from electrical resistance along the length of the cable like you have with analog cables pushing a signal over a copper wire. The amount of signal lost over optical should be virtually zero. Even better than that, is it's a digital delivery system. So you don't have the signal being converted from digital to analog, sent over the wire, then converted back to digital from analog, just to be converted to analog again as it goes to the individual speakers. It can stay in a purely digital form until it gets sent to the speakers. Every conversion results in a little quality loss, and so the more data the receiver has to work with, the better the resulting sound. You shouldn't need to be a big audiophile to detect a subtle difference between the two.