No, not solved. Twilio can now send long SMS messages, but still cannot receive them properly.
Now that everybody has smartphones, which do SMS split and reassembly invisibly to the user, the 160 character limitation is more of a historic thing and users are not aware of it. In practice, most long SMS messages are outbound, because they're marketing messages or spam, so this isn't a problem for most Twilio users.
Technical details, for anyone interested:
Multipart SMS messages have a binary header which carries the sequence number info necessary for reassembly. The Twilio API for incoming SMS (https://www.twilio.com/docs/api/twiml/sms/twilio_request) does not pass that through. The user's application gets multiple message parts from Twilio ("For incoming messages that are greater than 160 characters, the sending carrier will break up the message behind the scenes before delivering them to us, so Twilio will treat them as separate incoming messages and deliver them to your application in the order we receive them.") but without the info needed to put them back together properly. So the customer's program processes the first part right, and is then confused by the disconnected chunks of text in the later parts.
The Nexmo API (https://docs.nexmo.com/index.php/sms-api/handle-inbound-mess...) does: see the fields under "Specific Parameters for long 'concatenated' Inbound". The parts may come in any order, but they have ID numbers and "part N of M" info, so the user can reassemble them. Twilio support once talked about doing reassembly on their end, but that was never implemented.
