Travel health insurance is not mandatory for people who do not need a visa to enter the Schengen area (including people from annex II countries like Brazil and people from other countries who hold a residence permit from a Schengen country).
The travel medical insurance requirement is defined in article 15 of the Schengen Visa code and then mentioned again in article 21 on the entry conditions that must be fulfilled to issue a visa. It's also one of the reasons to refuse a visa mentioned on the standard refusal form.
By contrast, it is nowhere to be found in the Schengen Borders code. In particular, article 5 of this code, on “Entry conditions for third-country nationals” mentions most of the conditions listed in article 21 of the visa code (valid travel document, purpose of stay, financial means…), except travel insurance. Lack of travel insurance is also absent from the standard refusal form in annex V.
The Borders Code is the regulation that applies to third-country nationals who don't need a visa and defines all the requirements that apply to them. This regulation is binding for all Schengen countries, whatever their embassies might have to say about it. There is therefore no legal basis for border guards or anyone else to require insurance from visa-exempt travellers.
Some comments mention the fact that Slovakia apparently requires travel health insurance from visa-exempt short-term visitors and that this “requirement” even made it to the TIMATIC database airlines use to find out about entry rules in various situations. I would not be surprised if border guards there actually ask to see some proof of insurance but that's clearly illegal. Neither Slovakia as a whole nor individual border guards are free to make up their own rules.
Of course, being insured is the easiest way to avoid unpleasant discussions and can be beneficial for other reasons but it's not a legal requirement for a visa-free short-stay in the Schengen area.
Note that Schengen visa holders do need valid travel insurance every time they enter the Schengen area. The reason for that is that the visa requirement itself is included in article 5 of the Borders code and a Schengen visa can be revoked at any time if the conditions for issuing it are not met anymore, thus making all the requirements of the Visa code relevant for entry in this case.
That's particularly relevant for multiple-entry visa holders who only have to prove they are covered for their first intended trip when applying for their visa. If they show up at the border with a Schengen visa but without insurance (e.g. on a subsequent trip), the border guards should in principle rule that the conditions for issuing the visa are no longer met and revoke it.
In practice, border guards do not always check that.