No, that’s not correct.
You have paid the IHS surcharge, so you are entitled to use the NHS for free, same as any UK citizen.
Things like needing private insurance and paying for treatment only come into play if you are on a visa valid 6 months or less that has no IHS surcharge (for example, a visitor visa or a fiancé visa). In that case, you would need to make sure you had paid for all treatment while on that visa, as an unpaid NHS debt of £500 or more (when you were not entitled to free treatment) would mean a visa refusal.
So, in short, you have nothing to worry about because your FLR(M) visa allows you to use the NHS for free, so you can use the NHS as needed without needing to pay or take out insurance, and it will have no affect on your visa or future visas.
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