I've played matches with items all the time, and I've never seen lag because of it.
A lot of people are Smashboards hate items for being items. Even if you just put on smoke balls on low, he'd probably quit and say that the smoke ball might give you an unfair advantage.
Just play however you want though.
thats actually really fun to do. Its really the only item i see as fair in a 1on1 match, the others are over the line. Hp recovery, damage boosts, throwables, etc are too great in 1on1 situations. On the same not, 4vs without items is flatout dumb.
Hands down, your survivability with items on is diminished to a microscopic level. Not really because of what the opponent does but more along the line of what pops up infront of you at the worst possible time (FRACKING BOMBOMBS!)