It looks like nested qupdating calls (calling qupdating from an updating function) resulted in not returning data back via web.

Now I have:
global
procedure WebExtraAPI()

begin
WebStoreTabInvoice;
end;

procedure WebStoreTabInvoice()

begin
...
qupdating.ImportSalesInvoicesFromArea(...);
...
end;


global
updating procedure ImportSalesInvoicesFromArea(...)
begin
...
if (/*qupdating.*/SaveImportedInvoice(...)) then begin ... //commenting out qupdating helped?
...
end;