Can all mammals swim?
With respect to the giraffe claim, this article seems relevant:

D. M. Henderson, D. Naish, Predicting the buoyancy, equilibrium and potential swimming ability of giraffes by computational analysis, J Theoretical Biology 265 (2010) 151-159.

It cites several non-"random person on the internet" claims that giraffes cannot swim:


  It is generally thought that giraffes cannot swim, but relevant
  observations are few. Shortridge (1934) and Goodwin (1954) state that
  giraffes were poor waders and unable to swim. Crandall (1964)
  discussed a case where a captive giraffe escaped from a carrying
  crate, ran to the end of a jetty, and fell into the water. The animal
  reportedly sank without making any attempt to swim. MacClintock (1973,
  p. 54) stated ‘Giraffes cannot swim. Rivers are barriers they do not
  cross’. Wood (1982, p. 20) noted that ‘Because of its extraordinarily
  anatomical shape the giraffe is one of the very few mammals that
  cannot swim – even in an emergency! Deep rivers are an impassable
  barrier to them, and they will avoid large expanses of water like the
  plague’.


They then go on to show that a model giraffe could plausibly swim, writing: "For practical and ethical reasons we are unable to use live giraffes..."

They conclude:


  In summary, the results and speculations of this study show that it is
  not impossible that a giraffe could propel itself in water, but in
  terms of energy efficiency relative to that of the horse, it would
  appear that the costs of aquatic locomotion might be too high. It is
  reasonable to expect that giraffes would be hesitant to enter water
  knowing that they would be at a decided disadvantage compared to being
  on solid ground.