Grammarly corrects sentences like "He argued that sickness was a problem." and wants "be" instead of "was".
Seemingly, the rule is that as long as there is a noun phrase before that and after was, it requests a subjunctive ("be"). It is even flagged as a critical error and not a recommendation.
For me, this seems strange. It is not necessarily hypothetical (the arguer could well be right) and just sounds wrong to me. Is there a good delineation of the necessity of a subjunctive out there?
The subjunctive is generally used to express a requirement, necessity, recommendation, etc. (See Is It possible to use passive voice in the infinitive form without "to"? and https://ell.stackexchange.com/questions/132976/subjunctive-mood .)
It is necessary that he be there.
I recommend that she visit.
We require that he be watched.
In American English, the subjunctive is generally considered mandatory in such sentences. In British English, the phrase "should be" is generally used instead, or sometimes the ordinary indicative is used. (The subjunctive is acceptable in British English too, but less common.)
Often the phrase can be worded to avoid subjunctives:
It is necessary for him to be there.
We require him to be watched.
So, the "mandative" subjunctive can be used (and in American English is virtually compulsory) in expressions such as "he ordered that ... be done".
However, your example is quite different. "Argued" doesn't normally have a mandative meaning. Perhaps, if you interpreted "argued" to mean "recommended", you could use a subjunctive here, implying that a course of action was being recommended. But if you interpret "argued" to describe what someone believes and what line of argument they're putting forward (and this is obviously the case in your sentence about sickness), then clearly it shouldn't be followed by the subjunctive, any more than "thought", "said" or "believed" would be.
See also: https://en.oxforddictionaries.com/grammar/when-to-use-the-subjunctive
(Note: on rare occasions, the subjunctive "be" is used in a non-mandative way in formal writing; an example on the Oxford site is "Unlike rival international fairs, be they in London, New York or Maastricht, the Biennale has enormous popular appeal".)
