I regret this may be too late for your friend (though if so I would appreciate feedback) but, if not, suggest you have little choice other than to apply for two J-1 visas. What was written when the B-1 visa application was rejected might be of some help, since it would have been kind of them to indicate at that point that a single J-1 would be sufficient (if so) but I think understandable if the rejection did not include such advice.
USA sees some 38 million Overseas Non-Resident Visits (Provisional 2015 figures from the National Travel & Tourism Office, Business vs. Pleasure Travel spreadsheet). Analysis of the data here indicates a total of ~260k J-1 participants in 2014 across all states and 14 categories, which is already well under 1% of the visitor number above (which is after excluding more than 'the same again' from Canada and Mexico). The category I think relevant here (Trainee) is less than 10k, so of the order of one hundredth of 1% of all visitors.
Add to that two short courses in rapid succession with different sponsors and I'm afraid the situation is so unusual there is probably little familiarity with precedent etc, even amongst those issuing visas. Asking at a Consulate might be advisable but I would still not rely on what was said unless they were given time to do (and did!) some research, so for most people that might not be practical due to time constraints. A better approach might be to ask a sponsor to enquire on the traveller's behalf, since I suspect be a 'shortcut' to someone who knows. Between them the 10k shared a mere 55 sponsors.
Meanwhile I suggest the best option would be to apply for two visas. It should then be clear what you are doing, and why, and if the second application is rejected (rather than refused) as not required I can't see that you would have lost much (perhaps just the fee).
My concern is partly the terminology for the 30 days. 'Grace period' implies some kind of concession (though I appreciate it is formalised and all 'above board'). I fear using that time for a second course could be interpreted as at least exploiting a loophole, even if not against the rules.
The last part of the quote you mention in order to reenter the U.S. for the 2nd program I think is likely to be an 'approximation' – resulting from odds as above. Misleading for a case such as yours but failure to insert an "if necessary" does not make it incorrect.
An administrative issue might play a part. J-1's are tracked by State and sponsor, so a single J-1 for two courses if say in different States could complicate recording of statistics.
