Firstly, I would quote from a Bauddha śāstra 南海寄歸內法傳 i.e. preserved in Taishō canon, numbered T. 2125. In this śāstra, Yijing (7th-8th century CE), a Bauddha bhikṣu from China details practices relating to Mūlasarvāstivāda Vinaya and general daily life practices of bhikṣus in India (majorly), based on his experience in India. Although focus is on the practices of Bauddha bhikṣus, but most of the secular practices (such as latrine, chewing toothwood, etc.) mentioned in the śāstra, confirm with the practices of common people of that period, as pointed out by the author himself many times in the śāstra.
Water is used differently for pure and impure purposes, and it's kept
separately in two bottles. Earthenware or porcelain bottles are used
for keeping water for pure purposes, and copper or iron ones, for
impure purposes. The pure water is kept for drinking in the afternoon,
while the impure water is needed for washing after going to the
latrine. The pure water bottle must be held with clean hand and be
stored in a clean place, and the bottle containing water for impure
purposes should be grasped with an unclean hand and be put at some
unclean place. Only the water contained in a clean bottle, or in some
new and clean vessel, is fit for drinking in the afternoon, while the
water contained in other vessels is called 'timely water', which can
be drunk without fault at noontime or before noon, but it's faulty to
drink it in the afternoon. The water in the toilet jair is unfit for
putting into the mouth or to the lips. After going back to one's
chamber, one should rinse the mouth with water from a clean jar
(after answering call of nature). In case one has touched the toilet
jar after having finished the affair (of excretion), one should
again wash one's hands and rinse one's mouth; then one may touch other
utensils.
Clearly, there were separate bottles/containers for śuddha & aśuddha water, depending on the purposes each were used for. The bottles which contained water for activities such as defecation, were not used drinking water, as the water would be aśuddha by contact with those kind of bottles. Furthermore, Manusmṛti (5.127-128) clarifies what are śuddha objects as well as the fact that even śuddha water may turn aśuddha in contact with aśuddha objects. -
trīṇi devāḥ pavitrāṇi brāhmaṇānāmakalpayan /
adṛṣṭamadbhirnirṇiktaṃ yacca vācā praśasyate //
āpaḥ śuddhā bhūmigatā vaitṛṣṇyaṃ yāsu gorbhavet /
avyāptāścedamedhyena gandhavarṇarasānvitāḥ //
Since śuddha water may turn aśuddha in contact with an aśuddha vessel, thus proposition B is invalid. As for proposition A, it's discussed as follows-
That is, the original purity of the water gets lost due to getting in
touch with the container whose purity is questionable.
This statement is true, in line with what's stated earlier.
The water is as pure as the container in which it is stored.
But this line isn't valid in all cases because aśuddhajala may be stored in a śuddha container too. The śuddhatā of water is not ascertained only by the container it's placed in. However, placing aśuddha water in a śuddha container wasn't clearly the norm in olden times, as per Yijing. In that case, proposition A would be valid, but it lacks universal validity.
