Rainman,
Having a wider tire than rim always matters! If the tire is not wider than the rim it will not get "round", a tire that is not round will not corner right because it messes up the geomtry of the turn. A tire that is circular will contact the road in a fixed relation to the lean of the bike, a tire that is oval will have a continually changing relation to the lean of the bike, ( man this is hard to explain without drawing pictures). In other words a round tire gives a predictable turn, an oval tire gives an unpredictable turn, it will make the bike feel like it's diving one second, sluggish the next.

Round tires tend to roll better too!

A tire that is wider than the rim is much easier to mount and dismount than a thinner one.

A wider tire gets far less pinch flats and less rim damage from impacts and conering improves because of the larger "contact patch" as well