Presumably you don't trust the CA that signed the certificate on the server at the company you're visiting. As long as you heed the certificate error and don't visits the site, you're fine.
Now suppose you are a contractor who did some work for company A, then went to do some work for company B, and still have some cookies set from A's internal site.
Yep, ambiguous addressing doesn't save you, same as 10.x IPv4 networks. And one day you'll need to connect or merge or otherwise coexist with disparate uses if it's a common one (like in .internal and 10.x)...
IPv6 solves this as you are strongly recommend to use a random component at the top of the internal reserved space. So the chance of a collision is quite low.
There's usually little reason to use reserved space vs internet addresses, unless you just want to relive the pain of NAT+IPv4. The exception is if you lack PI space and can't copy with potential renumbering.
