Problem:

There's a story going round the news about a baby that was, apparently, cured of HIV using a cocktail of drugs at an early age. The story piqued my interest, but details seem scarce.

One of the main things I've seen being refuted about it is the difficulty in proving that
(a) the child actually had HIV in the first place, and
(b) that the child is really fully cured.

I've seen the following arguments:
Western Blot tests on young children are practically useless, since they test for antibodies. The child will likely have antibodies passed down by the HIV+ mother, regardless of whether the child has HIV. The test will show the antibodies, which may be mistaken for an active immune response from the child. As such, there will be a high false-positive rate on such tests.
Using PCR to attempt to identify a lack of HIV is flawed, since it may lay dormant in a small colony of T-cells until a secondary immune response is triggered, causing a new outbreak. As such, it is very difficult to show that a patient is "cured".

Required:

Question 1: Are these arguments valid?

Question 2: Are there any other reasons to be sceptical about the claims?

Question 3: Any other information that might be useful in understanding the case?