By the bed means each student signs their own lease for their own bedroom, with shared use of the kitchen, living room and bathrooms. So yes, four leases on one house. Each tenant is responsible for their own rent only. If one of the four leaves or stops paying, you're short $650, and the other three keep paying their own amount. Compare that to leasing the whole house to one group on a single lease where all four are jointly responsible for the full $2,600. Both models exist. By the bed is the standard in purpose-built student housing, meaning buildings designed for students from the start.
On the parental guarantee: a guarantee is a separate promise, usually from a parent, to pay if the student doesn't. It reduces credit risk, which is the risk of not getting paid by someone who lives there. It does nothing about vacancy, which is the risk of nobody living there at all. Those are different problems and the guarantee only touches the first one.
The part that catches people new to this is the calendar. Student leases usually run for an academic year, often 11 or 12 months, and nearly every lease in a campus market starts and ends the same week in August. If a bed is empty in September you generally hold it empty until the following August, because students don't move mid-semester. So one missed leasing season is a full year of lost income on that bed, not a month.