Wider tires can hydroplane easier, but for the question of producing more grip. A larger contact patch will create more traction. What you're family friend might be talking about is what happens on an improperly set up suspension. A lightly sprung car and a heavily sprung car will have a tendency to produce less grip as the suspension will either let the car roll too much (lightly sprung and damped) reducing contact patch as the wheel changes camber and toe characteristics. If the suspension is too heavily sprung, the tire can leave the ground as the suspension just won't be able to fulfill its design properly. Suspension tuning is all about understanding what your car needs for the conditions it's being driven in.
If you want some good articles to read regarding suspension, I suggest:
Sport Compact Car's "Make it Stick" series by Mike Kojima
This was originally run in Sport Compact Car magazine, but is thankfully hosted on Modified's site now that SCC is no longer. Kojima is a chassis engineer who's been working on Japanese imports for a very long time. Man knows his stuff.
MotoIQ's extended series on suspension design by Mike Kojima
Not to hump Kojima's leg, but he has written the best guides to suspension design I can find on the internet. They're by no means the end all, say all, but for the average gearhead, you can definitely take a lot away from his words.