even if not true, your hypothesis has the merit of rethinking 'estabilished facts'.  

It is clear that lack of knowledge is not the problem. Also, although Israel never had the hability of run something on the original Manhattan Project scale, the industrial effort of building an A-Bomb become much smaller with tech advances and experience. Building a bomb in the 60's must have been much easier than in the 40's, and quite more difficult than today.

So, the most relevant issue to answer "could Israel build A-bombs' in the 60's" is: given 60's tech, how much industrial effort, $  and U ore would be needed to build a few dozens of bombs? Would that be achievable or it looks like a bluff? I do not know enough to answer. 

Today Iran has all the drama with centrifugues, cyber attacks and so on. It is not THAT easy. 

Iran is relatively competent. Do you know it is on top 30 countries in robotics papers? 
https://www.researchgate.net/figure/RESEARCH-OUTPUT-BY-COUNTRIES-ON-ROBOTIC-TECHNOLOGY_tbl2_324829090