I've owned seven different bikes of all levels (from the cheapest POS $100 Walmart special to my current carbon-fiber-frame, Ultegra-equipped Specialized Sirrus LTD) in the past 15 years, and each and every one of them has chain-rub when crosschained, if the derailleurs have been adjusted properly.

The only time they don't chain-rub in cross-chain is when the derailleurs are out of whack.

Just don't cross-chain. Bike drivetrains are not designed to operate optimally in that mode.

As far as the slight chain-rub when you are using your middle chainring / smallest cog combo, use the barrel adjuster along your FD cable routing and give it a quarter-turn more tension. The higher tension will make the derailleur move outside just a hair more and eliminate the chain rub.