Absolutely - what Matt said. The "fyrd" means "expedition" - it's an offensive, aggressive army. That means men who have been born and bred to fight and command (I'd hesitate to say "professional" warriors), with the time to exercise, hunt etc, and the money/land/inheritance of spears, helmets, shields, probably a sword and certainly a horse or two.
Alfred's military reforms expected every five hides of land to provide one man for the fyrd, with spear, shield, helmet, sword, horse and a pound in money for his wages. We're not talking joe public - a fyrdman was a farmer in that he owned a lot of land and told people what to do, ie a landowner, not a worker!
That said, the later ninth and earlier tenth century saw considerable investment in fortified settlements (boroughs). The Burghal Hidage works out (quite accurately) how many hides of land each burh needed to provide sufficient men to defend its walls (one man per 'pole' of wall, IIRC). Looking at the way fortifications were used on both sides of the Channel at this point, the early boroughs may have been places of refuge for a set area (certainly how they were used in Flanders). They also served as centres for royal administration (with mints, taxmen, royal reeves, places for transactions to be witnessed etc), but they seem to have grown into population centres (ie "towns") more slowly, over the course of the tenth century. So, in Alfred's day a region under attack might well have seen "joe public" engaged in warfare... but with a very specific, limited role.
Since people were likely to head to a fortified place (with family, goods, cattle etc), you might well see armed civilians standing on the top of a wall looking menacing. It doesn't take a great deal of skill to stop someone climbing up a ladder - having a wall to stand on levels the playing field considerably! While joe public kept the vikings out of the boroughs, the fyrd was to assemble and attack the vikings. Without siege machinery, capturing a borough meant a determined assault or starving them out. The former would probably mean casualties if there was any serious resistance; the latter meant giving up mobility and becoming a target for the field army. It worked - only one of Alfred's boroughs fell (in the 890s, and it was still under construction).
As Matt says, the whole "fyrd = joe public" thing is an outdated myth - one of those lovely Victorian ideas which got into the public consciousness and are a right pain to dislodge. There was an assumption that, since the Anglo-Saxons were terribly nice, democratic chaps, with popular assemblies and practically a constitutional monarchy, they didn't have a standing army. When Johnny Foreigner turned up, the populace spontaneously formed an army and trounced them. Just like the 'modern' British, really. Various post-WW2 historians attempted to reconcile this received wisdom with what the evidence actually said (pointing strongly to a distinct military aristocracy), muddling things further with the "great fyrd" and "select fyrd".
More recent scholarship (particularly using Domesday evidence) shows that England was an extremely stratified place with lots of lordship and heirarchy. The Normans may have changed the personnel a good deal, but the actual structures of lordship (I won't use the f-word here!) were definitely not new.