The context is the following: The characters are watching TV and they give an interview to a guy that is over 40 and never had a lover.
One of the characters watching exclaims this.
As far I'm aware 滅多に is used with negative, how does fit this sentence? I gather it's akin to "That kind of people are rare"?
This is a rhetorical question where the implied meaning is negative. The actual message here is そんな人は滅多にいない. Therefore, even though there is no explicit negation in the sentence, I feel this sentence is acceptable. (But a sentence like this is not very common.)
When expressing a purely affirmative statement like "There are a lot of people like that", we never use 滅多. そんな人は滅多にいます is ungrammatical.
EDIT: Here are similar rhetorical questions where negative polarity items (NPIs) are used without explicit negation:
滅多 carries the sense of "unrestrained." Some say it was derived from やたらめったら, which of course is related to やたら but is closer in meaning to むやみ. While it's true that 滅多 is usually used in a negative sentence, at least till the time of 夏目漱石 it was also used in an affirmative sentence as we can see in the following examples, both from 吾輩は猫である.
「食べる事はどうせ食べるが、こいつは何だか先が欠けてるじゃないか」
「それだから早く持って来ないと心配だと云うのです」
「なぜ？」
「なぜって、そりゃ鼠が食ったのです」
「そいつは危険だ。滅多に食うとペストになるぜ」
いよいよ山の芋を盗むなと思ったら、しかもこの好男子にして山の芋を盗むなと思ったら急におかしくなった。しかし滅多に声を立てると危険であるからじっと怺えている。
Since it normally refers to an unrestrained act, using it with a verb of existence such as いる would have been uncommon even then. However, I personally don't think it would be a huge stretch to understand "unrestrained existence" as "abundance" or "commonplace." Besides, the sentence in question is formulated as a rhetorical question suggesting the speaker doubts such a person exists (in an "unrestrained" manner). So, it does have a negative sense. My final verdict on the sentence would be, while it's uncommon and sounds a bit archaic, it's still acceptable.
If we are to express the idea of 何ひとつ理解できるか (taken from one of the other answers) with the same level of (lesser) negativity as the sentence in this question, we would be saying 何ひとつ理解できるもんですかね. I find this much less acceptable. So I would think lumping 滅多 into the same category as such clear-cut NPIs as 何か, ちっとも, 少しも, etc. is, at the very least, misleading.
It can be understood more literally. 滅多 does not have to pair with ない (even if it often does).
２ ごく当たり前であるさま。並大抵。「—なことでは驚かない」
Thus そんな人めったにいるもんですかね literally translates to "Such a person ordinarily exist?". (Probably ordinarily is not correct strictly speaking). The more often seen めったに...ない can be understood not normally found=rare.
