There's a misunderstanding here. What the DMI displays is the same in Level 1 as in Level 2 (except for the Level icon). The difference is that Level 1 uses switchable balises in the four foot to transmit info regarding the End of Authority (EoA) etc. to the train, much like GW-ATP, in effect telling the train what the next signal aspect is. The info regarding the EoA is therefore only updated when the train passes over a balise group.
Whereas Level 2 uses the GSM-R datalink to transmit this info from the radio block centre (RBC - the signal box if you like) to the train. So if a signal ahead steps up/the section ahead clears, the EoA is updated almost instantly. In Level 2, the balises are fixed, transmitting data on position, national values etc. but nothing about where the EoA is - that info comes from the RBC via GSM-R
The transmission of data to the train is therefore intermittent with Level 1 but continuous with Level 2. This is reflected in the icons for each level: the Level 1 icon has a broken line indicating intermittent, while the Level 2 icon has a solid line indicating continuous.
Neither relies on linside signals strictly speaking, but I can't see much point in a 'signals away' implementation using Level 1.