Yes the example on the website is wrong. From the
partner earning chart.
LAX-ORD in discount economy is 25
ORD-FRA in discount economy is 35
Total 60
If LAX-ORD-FRA is booked as LAX-FRA on a single flight number then you'll only earn 35 airpoints dollars. If it is two flight numbers, or with a stopover (of a day or more) in ORD, then you earn 60 regardless of whether it is all on one airline (UA) or on 2 airlines (UA + LH).
Note some booking classes may be ineligible for airpoints earning (GINOX on UA and EILNORX on LH of which only G on UA and EL on LH are normal paid fares).