No, the issue you’re referring to applies to anything estimated directly from a sample; there’s nothing magic about zero or one. If you see 5000/10000 heads, the maximum likelihood estimate for that proportion is 0.5, but it still has some uncertainty attached: the 95% CI is about [0.49, 0.51]. With more data, you can shrink that interval, but you can never collapse it completely. On the other hand, that same data does let you assign exactly zero probability to the hypotheses “the coin is all heads” and “both sides of the coin are tails”, since you’ve seen counterexamples of both.