If one says or writes "suggesting he went away and came back", then it really means that one is suggesting that the truth is that he went away and came back.
I agree with the article. As an American English speaker, I would use the base form of the verb in the situation outlined in the language article you posted. And this is not because I want to prescribe correct grammar. This is simply what sounds better and more natural to me. I would, however, take it further to explain why it sounds better and, therefore, why it's correct.
Use the "traditional way", as the article calls it. If you are speaking or writing for a U.S. audience, you can't go wrong. And though this language change is well under way in Britain, as the article suggests, you can still use the "traditional way", as no one is bound to criticize you for this. Still, if you want to speak and write British English, then you could use the "non-traditional way", but be consistent. If you want to speak and write American English, then stick to what we would refer to in this case as subjunctive. This is a very fine point, but nonetheless an important one. It's a fine point because it is only obvious and apparent that there is a present subjunctive in English when we use third person singular, in which case we drop the "s", and when we use the verb "be", for which we use the base form, meaning the verb doesn't change.
It's important that we be clear about what we will accept when we begin negotiating the contract renewal.