I think it's worth clarifying a misconception behind this question, which in turn will answer the question.
Kashrus of milk can be divided into 3 categories:
1) Chalav Akum- milk which has no supervision upon it. As expressed in Y.D. 115 Chazal forbade this milk due to concerns that non-kosher milk may be mixed in. No one permits this today.
2) Chalav Yisroel- milk which was supervised by Jews. This is what is Chazal required in order for milk to be kosher. See Y.D. 115 and the commentaries for details- does a Jew have to watch the whole thing, or only the beginning, or just be present (even if he can't actually watch the milk go into the containers etc.) While there are these different standards discussed by the poskim, everyone agrees that you need Jews to be involved. (there are certain lenient opinions which are discussed in the context, but the accepted halacha is as mentioned above.)
3) Chalav "Stam"- this is what is very common today. There's a major shailah whether we could rely on government supervision of milk to ensure that nothing was added.
This is a middle ground case. On the one hand, Jews aren't supervising the milking so it's not exactly what Chazal required.
On the other hand, by a government body taking responsibility for ensuring the purity of the milk, we can be sure that nothing was added. There's a halachic precedent that אנן סהדי, a widely know fact, can sometimes be the equivalent of actual testimony. Can we apply this to today's milk?
This is a controversial question with many authorities taking both sides. Most famous among the lenient poskim is Rav Moshe Feinstein who wrote numerous teshuvos defending the lenient approach. See Igros Moshe Y.D. 1:47-49 (see Y.D. 2:35 that "baalei nefesh" should be stringent) and Chazon Ish Y.D.41:4 who leans towards the lenient opinion. (I have heard from talmidim of both Rav Yisroel Gustman and Rav Chaim Pinchas Scheinberg zatza"l that both rabbonim also agreed that in principle the strict halacha is to be lenient.)
According to these lenient opinions the milk is the equivalent of being cholov Yisroel; since otherwise it would be forbidden to be drunk.
However, there are many rabbonim who ruled that government supervision is not good enough to be considered cholov Yisroel; see Chelkas Yaakov Y.D. 34, Minchas Yitzchak 1:138, 2:21, 10:31:16 and Teshuvos v'Hanhagos 1:441.
So your question really boils down to the above dispute.
In order to be kosher for Passover, it is only necessary to be certain that there is nothing problematic about the food. Actual supervision is not required if it's possible to ascertain that fact through other proofs (checking out ingredients, government regulations etc.)
For milk this is the matter of dispute as mentioned above- is it enough to know that the milk has nothing non-kosher, or is there an actual requirement to supervise the milk?
Therefore even the lenient opinions (which have been widely adopted) only use the term "Chalav Yisroel" to refer to milk which has been actually supervised. Otherwise they would refer to it as "chalav stam"- not chalav akum which is prohibited, but not chalav Yisroel which has been supervised.
See here for more on this topic including additional sources.