The mouth is not a separate compartment. In advanced gum disease the total surface area of the pockets corresponds to a wound roughly the size of a palm, and that surface is continuously inflamed. The relationship between that inflammation and the rest of the body is a researched question.
The strength of the evidence varies by topic and is worth reporting without overstatement. The strongest data concern diabetes: the relationship runs both ways, and measurable improvement in glycaemic control has been shown after periodontal treatment. In diabetic patients, gum treatment should be seen as part of diabetes management.
The link with cardiovascular disease has been shown consistently, but it is an association; gum disease has not been proven to cause heart disease. Shared risk factors — smoking, age, diabetes — may explain part of it. A source that speaks with certainty here is claiming more than the evidence supports.
In pregnancy, hormonal changes heighten the gingival response and pregnancy gingivitis is common. Oral hygiene and regular check-ups matter during that period. Scaling and urgent treatment can be carried out in pregnancy; elective cosmetic work is postponed.
Associations have also been reported with respiratory disease and rheumatoid arthritis, where the evidence is more limited.
The practical conclusion: gum treatment is a health matter rather than a cosmetic one. Your general health and your medications are asked about at the consultation — that is part of the plan rather than a formality.