It usually does. There can be no definitive answer because as noted in the 14th edition of A Complete Course in Canning and Related Processes there's no international standard for condensed milk. So it depends on the national/regional standards how much milk must there be in it. But the book does give some usual industry figures:
In the manufacturing of sweetened condensed milk, standardisation to a definite percentage composition may be accomplished in three separate steps—the first standardisation establishes the desired ratio of fat to solids-not-fat of the fresh milk; the second establishes the desired ratio of added sugar to total milk solids (approximately 16½ kg of sugar is added per 100 kg of milk if the milk is to be condensed to 30% milk solids, whereas about 18 kg of sugar is added if the milk is to be condensed to 28% milk solids); and the third adjusts the concentration of the finished product to the desired percentage of total solids.
Some manufacturers prefer to slightly overcondense and then standardise back to the concentration desired by the addition of a calculated amount of water or skim milk.
So, yeah, according to the usual manufacturing process, most of the mass of condensed milk... originates from milk. A less scientific article which reiterates the same, but also explain the difference with "evaporated milk":
Both evaporated and condensed milk begin as fresh milk. The milk undergoes a vacuum process that evaporates over half the volume of water and concentrates the nutritive part of the milk. Evaporated milk is then poured into cans that are heatsterilized to prevent spoilage. The ultrahigh temperatures of sterilization cause the milk sugars to caramelize and give evaporated milk its characteristic cooked taste. In the end, evaporated milk has the consistency of light cream and a tint that ranges from ivory to pale amber.
Condensed milk is basically evaporated milk with a lot of sugar added (up to 2-1/3-cups per 14-oz. can) before it’s canned. The result is a thick, gooey, and intensely sweet product. Since large amounts of sugar prevent bacterial growth, condensed milk doesn’t need to be heat-sterilized and has a less caramelized flavor than evaporated milk.
Despite their similar packaging and nomenclature, evaporated and condensed milk are not interchangeable. Evaporated milk can be reconstituted with an equal volume of water and used to replace fresh milk in most recipes.
Due to its high sugar content, the primary use for condensed milk is in sweets.
And the Encyclopedia of Food Sciences and Nutrition has a bit of background story as to when the naming difference originated:
The basic process for preservation of unsweetened condensed milk by heat sterilization was conceived by John B. Meyenberg in 1882, a Swiss citizen, and an employee of the Anglo-Swiss Condensed Milk Company. The idea of preserving milk without the addition of sugar was made possible by his invention of a revolving sterilizer working with steam under pressure. Lacking sufficient support from his company to continue his work, he migrated, in 1884, to the USA and also obtained a patent for his invention in that country. In 1885, Mr Meyenberg was cofounder of the Helvetia Milk Condensing Company in the State of Illinois, and during the same year, he achieved the first successful manufacture of unsweetened condensed milk. The name of this product was changed to evaporated milk for a clearer distinction from sweetened condensed milk, a situation that prevails today.
It's not clear to me what terms were used in Indonesian (for one vs the other variety), but presumably the latest regulatory effort is to create a similar distinction. In any case, the clear intent of the regulator is to stop sugar-added condensed milk being sold as milk. Another reporting on the same from JakartaGlobe:
According to Damayanti Rusli Sjarif, the head of nutrition and metabolic diseases at children's health department of the University of Indonesia, condensed milk is used all over the world for producing pastries, cakes, ice cream, not as a milk substitute.
"In Indonesia, however, sweetened condensed milk is given to children and infants as an alternative to formula milk," Damayanti said.
Recent studies by Unicef, Asean and WHO concluded that one in eight Indonesian children is overweight, with a major contributing factor being the consumption of dense processed foods, including condensed milk.
More than 50 percent of sweetened condensed milk is just sugar, and 100 grams of it account for 18 percent of the recommended daily intake of carbohydrates.
Oddly, none of the 3 Indonesian news stories (in this Skeptics page) mention evaporated milk, so I'm guessing the latter might have very poor market penetration in Indonesia.
Australia and New Zeeland have a common standard for what constitutes condensed and what evaporated milk:
2.5.7—3 Requirement for food sold as condensed milk
(1) A food that is sold as condensed milk must:
(a) be condensed milk; and
(b) contain no less than 34% m/m milk protein in milk solids non-fat.
(2) A food that is sold as condensed whole milk and derived from cow’s milk must contain:
(a) no less than 8% m/m milkfat; and
(b) no less than 28% m/m milk solids.
(3) A food that is sold as condensed skim milk and derived from cow’s milk must contain:
(a) no more than 1% m/m milkfat; and
(b) no less than 24% m/m milk solids.
[...]
2.5.7—5 Requirement for food sold as evaporated milk
(1) A food that is sold as evaporated milk:
(a) be evaporated milk; and
(b) contain no less than 34% m/m milk protein in milk solids non-fat.
(2) A food that is sold as evaporated whole milk and derived from cow’s milk must contain:
(a) no less than 7.5% m/m milkfat; and
(b) no less than 25% m/m milk solids; and
(3) A food that is sold as evaporated skim milk and derived from cow’s milk must contain:
(a) no more than 1% m/m milkfat; and
(b) no less than 20% m/m milk solids.
So yeah, they impose (lower) limits on milk solids/proteins and (upper limits) on milk fat (for some varieties), but I guess they just rely on the customary market distinction for not getting sugar into evaporated milk, because there's no specific sugar limit in that standard that I can see. So I'm guessing Indonesia has had a somewhat unique problem with the condensed milk (marketing), at least regionally.
Also, to some extent, the viral story in Indonesia reminds me of the plastic sold as rice stories, which turned out to be bogus.