Depending on the opiate, they can cause cross reactions for certain tests.
Any opiate even partially derived from morphine will test positive for a morphine test. Any derived from codeine, codeine. And some tests can even cover BOTH.
That is the 'screening' aspect of the test. After that, they GC/MS the sample to determine specifically which opiate it is.
So yes, they can cause cross positives. But 99/100 times, once the first round of the test gets a flag, they will GC/MS it to determine PRECISELY what drugs, as well as to avoid false positives (which are eliminated entirely by GC/MS).
So they will know exactly what opiates you took, eventually. Especially if you make it a big point of "oh well thats not the one i took, go check!" they WILL GC/MS your sample, and will know youre full of shit.