I've just read the actual study and can see how it has been turned into gimmicky articles in the press but actually isn't all that impressive.
The women in the study were under 39. Other exclusions were of women with PCOS or other hormonal problems or moderate/severe male factor (mild was included). 20-25% received IUIs and most of those involved stimulation to produce 2-3 eggs(!). And a few had an IVF or even ICSI... (all included in the stats).
The authors did note that they followed up with the couples that had originally been excluded from their study and... pregnancy rates were the same (!).
Looking at ttc statistics, out of the couples who aren't successful in their first year, about 40% go on to conceive in their second or third year.
Given the pregnancy rates in the study and the proportion of couples that met inclusion criteria for the study, I think HSG only made a small difference that to me seems in line with the anecdotal evidence that I read about here and there. So I'd guesstimate at more like 4% than 40%.