Thanks for your answer Taylor,
The call account/verify_credentials failed both in 1 and 1.1 (HTTP code 401). So it seems clear my token is broken. Now asking for a new token (through account/authorize) actually works fine, but it means asking my customers to do a full OAuth dance 
I also tried header based OAuth, it leads the same error
curl --get âhttps://api.twitter.com/1.1/application/rate_limit_status.jsonâ --header âAuthorization: OAuth oauth_consumer_key=â0kOc7S4AXi9iaNyzLEv0Rgâ, oauth_nonce=âbe3d1969972b943b65d9b0fa7be5f3eaâ, oauth_signature=ârXi5n63UDIQTR%2FUxMmSbfHSWaRA%3Dâ, oauth_signature_method=âHMAC-SHA1â, oauth_timestamp=â1355520261â, oauth_token=â308930278-VxGlaF40PGIIHY9iOr6qurCdZkIAhRHLOSsnfURuâ, oauth_version=â1.0ââ --verbose