It's never free
The most direct answer to your main question is that an employee with a very large insurance claim could end up costing all employees of MoneySavers more "in the end" with either insurance approach. I used quotes on "in the end" because that phrase is doing a lot of work here.
Health insurance in a nutshell
The basic idea of health insurance is that large groups of people have fairly reliable average risk: you may not be able to predict that Bob, specifically, will break his leg this year, but you might be able to guess that one employee of MoneySavers will break their leg before the year is out. So the insurance policy will expect to pay out enough to cover treatment of one broken leg for all employees of MoneySavers in one plan year.
To cover the expected payouts, the insurance policy will involve charging all employees a premium for the insurance. This premium will be enough to cover the expected payouts (plus some padding, as expected health events and expected costs are both ranges rather than point estimates), as well as the costs of administering the insurance policy (which includes things like people processing medical claims, contacting employees, handling customer service questions, and so on), plus a profit margin for bearing the health-cost risk (in a fully-insured plan) and the administrative work that is done.
But the expected payouts are always estimates. Very methodically produced estimates which account for uncertainties, but estimates all the same. If the covered population (in this case, employees of MoneySavers) has higher than expected costs, particularly over a couple of years, it is likely that whomever is pricing the plan will recognize that they need to charge a higher premium to cover those higher than expected costs. This is the way that high-cost claims might end up costing all employees more: the insured population needs more money available to pay out enough to cover the claims incurred.
These are very simplified examples, but get to the basic idea of how coverage costs might increase due to an employee having high medical costs. The insurance policy needs to cover the payouts for incurred medical claims, and someone needs to come up with the money to do so.
Self-funded vs. fully insured
There are any number of reasons that someone in charge of choosing health insurance might choose either method, but some of the most relevant considerations are:
- Insurance pool size. A small employer (and 60 employees will count as
"small" for these purposes) is likely too small a population to
estimate risk very reliably, and so small businesses can be difficult
to price. They tend to be funneled into larger pools of many small
businesses that are insured by the insurer. You choose from among benefit packages that the insurer is already operating, or that they plan to sell because they believe they can operate those packages profitably.
- Benefit design. If you've ever had to choose a health insurance plan,
you are probably familiar with having from one to three options, any
of which may or may not suit your insurance needs. This is where the
larger insurance pool issue above comes into play. To be profitable,
an insurance plan that is offered to MoneySavers might need to
include benefits that MoneySavers employees don't really need (but
are necessary to keep other businesses in the pool for that benefit
package), or might need to exclude benefits that employees would
prefer to have (the need for those services might be too rare, for
example, or most insured people in that plan don't want to pay
premiums to cover those services). If you self-fund, you get a lot
more flexibility on benefit design, because you're ultimately paying
the cost when employees use those benefits. When you're in a pool with 100 other businesses, you're much more likely to get something like the average desired benefits across all of them.
- Cash on hand. Self-funding your insurance policy means that
MoneySavers will take a large amount of money and set it aside in
order to ensure that sufficient money is available to pay out for
insurance claims. Self-funded insurance tends to have stoploss
coverage (such as, they are responsible for up to $10 million to pay
out per year, but claim expenses beyond that are picked up by the
insurance company), but otherwise the money to pay for claims comes
from MoneySavers alone (however they want to arrange that), and not
from the insurer. MoneySavers, in this case, is bearing the bulk of
the insurance risk.
- Cost of services. You pay extra to have an insurance company bear
your medical cost risk (as in a fully insured plan), but even if you
self-fund you still have to pay for the administrative work the
insurer does, plus any stoploss coverage you've purchased.
The delicate balance
One of the constant tensions in health insurance pricing is between providing attractive benefits to members (like covering services that they are likely to use) and keeping insurance plans affordable enough for members to purchase (most visibly in the form of the monthly premium, though there are all sorts of cost-sharing shenanigans that tend to confuse consumers).
The more generous a plan is, in terms of both services a plan covers and how much of the costs it covers, the more it will cost to fund (so that claims can definitely be paid) and to manage (more covered services tends to mean more claims, and a larger provider network tends to mean more administrative overhead, etc.). But the more expensive a plan is, the less likely it may be that subscribers will choose to pay for it. So insurers tend to try to provide an attractive mix of coverage options within a constrained range of possible prices.
It surprises many people to learn that, while health insurance is a high dollar business (they deal with lots of money, after all) it tends to be a relatively low margin business (they are not raking in 50% profits). If the plan ends up underpriced, and outgoing claims outstrip the funding available to cover them (or erode the profit margin too much for comfort), the insurer will in all cases respond so that they do not continue to lose money indefinitely. This may not be immediate, and corrections can come in the form of reducing coverage or raising prices (among other strategies). This is true whether the insurer is an insurance company or if it is the employer itself. Neither has much incentive (or even ability, especially for insurance companies which are subject to various regulations) to spend unlimited money on the people they insure.
But we end up back at the header at the top of this answer: it's never free. If MoneySavers employees are more expensive to insure, then the cost of that insurance will be more expensive as well. Self-insuring does give more discretion to MoneySavers (the insurance company can't unilaterally change the benefit package), but that doesn't automatically make MoneySavers more capable of, or interested in, absorbing higher-than-expected medical costs.