Here an article in Luxemburger Wort of 07-11-1932 (right column below) which says Luxembourg and Swiss FA were negociating for years to arrange a match between the two countries
There are also this intersting words from Swiss FA president: "Es ist nicht Überhebung daß wir nur unsere B-Team zur Stelle haben. Unsere A-Team ist an die durch unsere Verhältnisse vorgeschrieben Bahnen gebunden, über die wir nicht hinausgeben können." Which can be translated as: "It is no Arrogance we only field our B-team. Our A-Team is bound by the conditions imposed by our tracks that we can not give out."
Unfortunately the article does not tell anything about the conditions. Taking Luxembourg's results against A-teams until 1932 in consideration it seems some teams would risk an embarrashing defeat against Luxembourg, at the time far the smallest European FIFA-member both in surface and population. France started to play its friendlies against Luxembourg with B-teams in 1922 (the results showed the same kind of pattern), Belgium in 1924, Switzerland in 1932 and some other countries after WW2.
29-10-1911 France L 1-4 Luxemburg
20-04-1913 France L 0-8 Saint-Ouen
08-02-1914 France W 5-4 Luxemburg
28-08-1920 Netherlands L 0-3 Vorst
29-05-1924 Italy L 0-2 Parijs
21-05-1927 England L 2-5 Esch-sur-Alzette
27-05-1928 Belgium L 3-5 Amsterdam
28-06-1928 Egypt D 1-1 Esch-sur-AlzetteBegium 5-3 Luxembourg at the 1928 Olympics in Amsterdam.