While gramatically correct, you cannot say "Hier überträgt Information" in german.
The reason is that Information is not the subject here -- the information does not do the act of conveying itself, instead something else conveys the information.
"Luft überträgt Information durch Schallwellen" "Information is conveyed in air by sound waves".
From my understanding [+ dictionary] 'broadcasting' describes a scattered distribution while 'conveying' works from a to only one b, instead of many, is that correct? In that case, 'to broadcast' would be senden, ausstrahlen, verbreiten. 'übertragen', in german, is more likely understood as transmitting or transfering, in my opinion. 'remote transmission' for example is translated to 'Fernübertragung', (see: http://en.wikipedia.org/wiki/Remote_data_transmission)
"Broadcasting" does mean widespread distribution. It's distinguished from "narrow casting" (a word that is not used frequently, except to contrast means such as cable with broadcasting), and, as you point out, it would never mean point-to-point transmission such as by telephone or by modem connection between two computers. But now I am confused. Why would "broadcast" be a wrong translation in the example?
Because 'broadcast' wouldn't be your first choice for 'übertragen', only in specific cases, like a tv show which is broadcasted. It's a possible solution, but not the best. Media broadcasts are the only example I can think of where this might fit. In German, a tv show (Sendung) is being broadcasted (wird gesendet or ausgestrahlt or sometimes übertragen, being my least favourite choice). The show itself is transmitted (übertragen) via cable or satellite and conveys or communicates (vermittelt) information or knowledge to the viewer. It's all different shades speaking of the same sort of action in a different context and range. leo.org offers even more, even sorts of physical movement from a to b as possible translations of 'convey', while all other translations of 'broadcast' depict the widespread and scattered distribution, 'übertragen' doesn't.
If you're curious about some more everday usage, one would even say 'When is »The Simpsons« aired?' - Wann kommen (lit. come) die Simpsons? An answer might be: Sie laufen um 20:15 - 'They run at 8:15 pm.' That's pretty colloquial and meant solely as additional insight. There's a wide range of words dealing with all these things and they depend a lot on the context.
Edit: Google research says, 'wann kommen die simpsons' gets 'About 2,500,000 results' and 'wann laufen die simpsons' at least 'About 859,000 results'.