The threshold for a perfectly secure system is that a computationally unbounded adversary cannot conclude anything about the plaintext from the ciphertext. With a public-key system, the attacker can try to encrypt messages with the real public key; this is not possible with one-time pads. What the attacker can do, quite simply, is to try all one-bit messages, then all two-bit messages, then all three-bit messages, etc., looking for a matching ciphertext.
Now, a public-key encryption algorithm may involve some randomness. The way to handle this is to try all possible outputs of the random number generator. You can make an algorithm $\textsf{Check(c,k,m,r)}$, where $c$ is the known ciphertext, $k$ the known public key, $m$ the guessed message, and $r$ is a string of bits. This runs the public-key algorithm with key $k$ on message $m$. Where the algorithm needs a random bit, it takes the first unused bit of $r$ (so it starts with the first bit, then the second, etc.), so the algorithm becomes deterministic. If all the bits of $r$ have been used and it needs another random bit, or if the encryption completes and the generated ciphertext does not match $c$, it returns False; if the encryption completes and the ciphertext matches $c$, it returns True. You can then run $\textsf{Check}$ with 1-bit $m$ and 1-bit $r$, then 1-bit $m$ and 2-bit $r$, then 2-bit $m$ and 1-bit $r$, then 3 and 1, then 2 and 2, then 1 and 3, etc. (i.e. the sum of the lengths of $m$ and $r$ is two, then three, then four, etc.) This will terminate with $\textsf{Check}$ returning True; when it does, you know what $m$ is.
