Non-residents must have a ticket from Schengen country to another destination and valid documents. Check TIMATIC!

Article 5

Entry conditions for third-country nationals

1. For stays not exceeding three months per six-month period, the entry conditions for third-country nationals shall be the following:
(a)
they are in possession of a valid travel document or documents authorising them to cross the border;
(b)
they are in possession of a valid visa, if required pursuant to Council Regulation (EC) No 539/2001 of 15 March 2001 listing the third countries whose nationals must be in possession of visas when crossing the external borders and those whose nationals are exempt from that requirement (17), except where they hold a valid residence permit;
(c)
they justify the purpose and conditions of the intended stay, and they have sufficient means of subsistence, both for the duration of the intended stay and for the return to their country of originor transit to a third country into which they are certain to be admitted, or are in a position to acquire such means lawfully;
(d)
they are not persons for whom an alert has been issued in the SIS for the purposes of refusing entry;
(e)
they are not considered to be a threat to public policy, internal security, public health or the international relations of any of the Member States, in particular where no alert has been issued in Member States' national data bases for the purposes of refusing entry on the same grounds.
2. A non-exhaustive list of supporting documents which the border guard may request from the third-country national in order to verify the fulfilment of the conditions set out in paragraph 1, point c, is included in Annex I.

[..]

ANNEX I

Supporting documents to verify the fulfilment of entry conditions

The documentary evidence referred to in Article 5(2) may include the following:
(a)
for business trips:
(i)
an invitation from a firm or an authority to attend meetings, conferences or events connected with trade, industry or work;
(ii)
other documents which show the existence of trade relations or relations for work purposes;
(iii)
entry tickets for fairs and congresses if attending one;
(b)
for journeys undertaken for the purposes of study or other types of training:
(i)
a certificate of enrolment at a teaching institute for the purposes of attending vocational or theoretical courses in the framework of basic and further training;
(ii)
student cards or certificates for the courses attended;
(c)
for journeys undertaken for the purposes of tourism or for private reasons:
(i)
supporting documents as regards lodging:
—
an invitation from the host if staying with one,
—
a supporting document from the establishment providing lodging or any other appropriate document indicating the accommodation envisaged;
(ii)
supporting documents as regards the itinerary:
confirmation of the booking of an organised trip or any other appropriate document indicating the envisaged travel plans;
(iii)
supporting documents as regards return:
a return or round-trip ticket.

Moreover, I stand corrected. There is a Schengen border codex, which actually requires some proof to make plausible how the US citizen intends to leave the EU in time.
A simple refundable ferry ticket Hoek, Belgium to Harwich, UK would have been enough.

That changes the story a bit. However, I am pretty sure that US citizen do not have to own an onward ticket for stays up to 90 days in the EU.

Here is my take on it (in case SN was the culprit):
1) Airline was wrong.
2) SN owes the passenger EUR 600 denied boarding compensation. (EC261/2004)
3) Passenger can decide whether to claim a full refund or a free rebooking to another date (EC261/2004).
4) A DOT complaint could be filed once the passenger obtains the information that no onward ticket is needed to enter Belgium for up to 90 days.
5) If the airline acts in bad faith (denying a free rebooking to another date), the passenger may claim consequential damages, as well.