I agree that MPLS would be used for transport through the Infineras, but the article specifically states that this was caused by management traffic.
MPLS doesn't have a concept of a broadcast address and wouldn't have been used for management traffic (except maybe during transit). MPLS is really just used to get IP packets to their destination with less L3 overhead. Full disclosure I work in the DC space, not the provider space so I'm far from an expert on MPLS.
Ethernet famously doesn't have a TTL, so maybe this was just a typical Ethernet broadcast storm. In that case I don't know why TTL would've even been brought up.
They keep throwing around the word packet, which implies layer 3. Of course lots of people say packet when they mean frame.
Edit: There is a comment above saying they have an RFO stating this was a broadcast storm. So it was probably Ethernet and CenturyLink brought up TTL as a way to blame the protocol.