Of course not, the problem is that capacity is consumed while the packets are in transit. Transfers are not (and cannot be) instantaneous. That transit times are short, to human perceptions, doesn't change the fact that it's limited and while you're downloading a file no one else can use capacity that you're consuming. If transfers we're (could be) instantaneous then you'd be correct, but they're not and will never be. In fact, as we increase the number of devices in the home network the problems get to be more severe since in addition to the bit rate limits there are also various physical limitations, like time slots in DOCSIS, that also limit the capacity in the network.
Now, that doesn't mean that Mediacom is correct, they're using a very poor analogy IMO, but again the argument that nothing is consumed in transit is also fallacious, just because the capacity is restored once a transfer is complete.