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 ‘https://api.twitter.com/1.1/application/rate_limit_status.json’ --header ‘Authorization: OAuth oauth_consumer_key=“0kOc7S4AXi9iaNyzLEv0Rg”, oauth_nonce=“be3d1969972b943b65d9b0fa7be5f3ea”, oauth_signature=“rXi5n63UDIQTR%2FUxMmSbfHSWaRA%3D”, oauth_signature_method=“HMAC-SHA1”, oauth_timestamp=“1355520261”, oauth_token=“308930278-VxGlaF40PGIIHY9iOr6qurCdZkIAhRHLOSsnfURu”, oauth_version=“1.0”’ --verbose