Well if they are doing a mixed private/public net then it wouldn't be like the addresses are routable outside of their network. I've seen a number of clients which were essentially 'natted' behind the ISPs infrastructure. At its core the ISP gets all packets landing at their router and if they want to advertise an 'inside' route to 1.2.3.4 (or 10.0.0.1) that is something they could do successfully.
Yep, you're right; a net with mixed public/private addresses can
certainly work well when done correctly. Unfortunately, it can also
seem to work for some period of time when done incorrectly. The
trouble is, most people don't grasp the ramifications of doing it wrong.
I'm sure you understand the ramifications at least as well as I do, and
probably a whole lot better, but for the sake of everyone else in the
room...
When a network/ISP misuses unallocated address space by routing
the traffic to something internal, this prevents the inside of the
network/ISP from reaching those addresses normally. Unallocated address
space can be allocated by the RIR's at any time, so misuse of
unallocated address space results in parts of the Internet unreachable.
If some huge networks/ISP's (Comcast, Verizon, Sprint, ...) decided to
misuse the address block allocated to you for some internal purpose,
you'd be rightfully upset since it would prevent all users of those
ISP's from reaching your service/servers. Now let's assume you're a new
company and just got a new allocation of addresses from the RIR only to
find out the users of major ISP's can't reach your service because the
ISP's have already misused your address block for something internal
on their networks. Yep, you'd be livid, and livid with good reason.
If you put a lot of work into your misuse of unallocated address space,
all that effort could turn out to be wasted a few hours later when the
block you misused gets allocated. To reach the newly allocated block,
you'd need to redo all that work over again, correctly.