First, unless you waive the requirement, before the 401(k) plan is permitted to make a distribution to you they are required by law to provide you with a statement of your options with regard to this distribution, including the details of your option to roll over this distribution. By not being able to providing you with this information they are in violation of this law. Perhaps it's just that the representative that you talked to is ill informed.
But to your question, the distribution that you receive after separation from service that satisfies the loan is an offset distribution that reduces the balance to your credit by the amount of the outstanding loan balance without giving you any money. It's equivalent to making a reportable, taxable distribution of cash to you from the 401(k) and you immediately turning that money around to pay off the loan. An offset distribution is reported with code M in box 7 of the Form 1099-R for the year in which the distribution occurs (possibly along with code 1 or 2 depending on your age).
What the 401(k) plan is required to tell you is that you have until the due date, including extensions, of your tax return for the year in which the offset distribution occurs to come up with whatever portion of the amount of the offset distribution you can and roll it over to another retirement plan, say, to your new employer's plan or to a traditional IRA, to continue to defer the taxes and possible early-distribution penalty on the amount rolled over.
Your new employer's plan is not required to accept rollovers, so you might have to roll it over to a traditional IRA instead.
