It's not true rather. According to book by Osprey publisher titled Slovakian Bulgarian Aces of WW2 in 1941 at least a few of Russian I-16s were shot down by pilots of the 12th squadron flown B.534s over Ukraine.
Concerning I-153.... victories over the plane were claimed by Jan Reznak - 4, Izidor Kovarik - 2, Frantisek Cyprich - 1, Pavel Zelenak - 1, Josef Stauder - 1, Josef Jancovic - 2. In addition each of these mentioned pilots here claimed a few of I-16s as well. But I'm not sure if these were scored when flying Avia B.534