Sharingan Genjutsus are certainly powerful, that much is clear. But all of them do not require eye contact, those most do. The way this is theorized to work is that with regular genjutsu, one must generally form handseals to initiate the Genjutsu, molding the chakra for this illusion through the seals. The mediums for genjutsu differ greatly, a large portion of them being visually triggered, such as looking at the user or a specific object. Some others are triggered through hearing a sound ( Namely Sound Genjutsu ), and even others are triggered through sense of Smell, Touch, and Lili extended this to the sense of Taste with her CC. With most Sharingan Genjutsus, this medium is Visual, requiring the user to able to cast a genjutsu through eye contact alone, however not all do this. A specific one that doesn't require eye contact would be (Doujutsu: Shiranui) - Eye Technique: Phosphorescent light. This one is triggered by having a line of vision with the target, being able to physically see him.
Shisui was a master of Sharingan Genjutsu and his Mangekyou Sharingan was shown capable of using Sharingan Genjutsu to great effect, able to cast Genjutsus on others without them even being aware of it, or without them even being able to see it, demonstrated by Danzo when he trapped Mifune in a genjutsu without him even being aware of it happening during the Five Kage Summit Arc. What that specific quote likely meant was that due to Shisui being hailed as the greatest Genjutsu user of the Uchiha, his prowess with it was so great that he was able to cast a Sharingan Genjutsu from greater ranges than others, possibly even normal Genjutsu as well. This however does not mean that normal Genjutsu is able to be cast through greater ranges than Mid range in the RP. Genjutsu is confined to Mid range whereas Sharingan Genjutsus, some of them anyway, have the possibility of being used at Long Range. The Sharingan is able to pierce through Visual Genjutsus as well as reverse other genjutsus cast upon the user. Starting with the first, Visual Genjutsus, are genjutsus that take on a Visual trait primarily. This means that Genjutsus that primarily are used to alter your sense of sight and what you are able to Visually interpret are considered Visual Genjutsus. Sharingans are able to break through this visual illusion with ease, due to their natural "piercing" abilities, allowing the user to see through it. How this is achieved isn't an exact science but we reason it to be along the lines of simply focusing your vision once you have reasoned it is an illusion and piercing through it with ease, an instinctive and relatively quick process, taking next to no time in the timeframe and being passively achieved. However, this is only viable for Visual Genjutsus. As for other Genjutsus that plague the mind, should you reason it to be a Genjutsu, you are able to reverse the genjutsu itself, though we will touch on this in greater detail later. Also, note my point about casting Genjutsu through the Sharingan above, it doesn't increase the range.
With that said, any questions before we move on to the jutsus themself?