Net::OAuth versions before 0.33 for Perl allow the sender to choose the signature algorithm in verify.
verify resolves the signature method class from the signature_method parameter of the incoming message. signature_method is required on every request, so the algorithm used to check a signature is chosen by whoever sent it, and nothing lets the verifying party pin the method instead. When a message names HMAC-SHA1 or HMAC-SHA256, the key is derived from consumer_secret and token_secret rather than from the key the provider deployed.
A provider deployed on RSA-SHA1 holds only the consumer public key, and RFC 5849 does not use consumer_secret for that method, so the required parameter is filled with a placeholder. A client that names HMAC-SHA1 instead has its signature checked against that placeholder, so a guessable one is enough to forge requests for any consumer key and token.
Upgrade to Net-OAuth 0.33 or later.