Seems to check out, for a small part at least:
With 80 men moved out, with 81 returned home
The relief at home was great: "Already in Nendeln the contingent of authorities, relatives and population was celebrated," says Geiger. And the legend is true: The 80 Liechtenstein soldiers came home with one more soldier whom the troop had won as a friend. "There are rumours to this day that he was an Austrian conscientious objector or servant looking for work in Liechtenstein," explains Geiger. That, on the other hand, is not true. The 81st man was an Austrian officer who accompanied the contingent as a liaison man and as a kind of guard of honour.
Als die Armee mit 81 Mann zurückkehrte
But when they picked up the foreigner, and of which nationality, seems doubtful. This claims "an Italian". This as well:
In 1866 they went to war for the last time, with 80 men they went out against the Italians. With 81 men they returned home - on the way they had made friends.
As it was at the time 'for the Austrians' and planned as against the Prussians, but ultimately guarding against Italians, either way cannot be ruled out.
At least, the "80 men marched out", is long accepted history.
Even if the identity or nationality of the new friend seems doubtful, Geiger is the author of numerous books on the matter and curator of the national museum of Liechtenstein.
Geiger, Peter: 1866 – Liechtenstein im Krieg – Vor 150 Jahren, Katalog zur gleichnamigen, von Peter Geiger kuratierten Ausstellung im Liechtensteinischen Landesmuseum (Mai – September 2016), Vaduz 2016, 96 Seiten.