What you heard about "group" doesn't actually have anything to do with belonging to an association or a group (for the most part). It's a type of insurance.
There are two main kinds of medical insurance - individual and group.
(1) Individual insurance is a policy you purchase yourself and is not connected to your employer.
(2) Group is a policy that is purchased by an employer (or similar type of organization such as a union).
If someone belongs to some kind of association, for example, the American Counseling Association (ACA), they might have a discounted medical insurance program available to members. But this is individual insurance that the individual purchases for him/herself - the policy is not purchased by the ACA.
When someone goes from "group" coverage to another "group" coverage with a gap of no more than 63 days, then pre-existing does not apply (for example, if I leave my job today and get a new job and am covered within 63 days then I don't have to worry about any conditions or pre-existing conditions).
However, if someone purchases individual insurance or group insurance and has no recent proof of coverage then they are subject to any applicable pre-existing exclusion or limitation.
If you were to get a job with an employer that offered medical insurance you would not need to answer any medical questions. But when a claim occurs the ins co would then ask for proof that the condition for which you are treating is not pre-existing. After some period of time, somewhere between 12-24 months, often pre-existing goes away. So if someone with no prior coverage started a new job and got medical insurance and didn't need any treatment within the next 24 months they'd likely never have an issue. If he/she broke his/her leg it wouldn't be pre-ex but if he/she went in for treatment of diabetes (or anything related) they'd likely say they can't cover it until they prove it's not pre-existing.
Individual coverage is different. You must complete a full medical questionnaire and provide medical records for whatever period they are asking for. Failure to provide those records, or the insurance company being unable to get them from the provider directly, often results in a denial of coverage. If the ins co does get all the records and evaluate they can do two different things (1) exclude any known conditions from any coverage at any time or (2) place a time period on which they won't cover those things.
So it's still good to get individual coverage though they may not cover any treatment related to mental health issues. But if they did grant coverage, with mental health excluded, then any physical illness/injury may be covered.
I hope this helps, and if I haven't hit on your exact questions please let me know.