The simple answer to your question is yes; the airplane should have been able to stop without thrust reversers. But it’s not that simple, thrust reversers may be involved in the cause of the accident. This is really an operations issue because the airplane is already certified.
Very basically, for dispatch purposes, thrust reverse cannot be included in the stopping distance, as well as only one half of head wind and 150% of tail wind component. There are other items involved such as designation airport runway slope (uphill or downhill), pressure and temperature different from standard at intended time of landing, as well as intended landing weight. From this information you must be able to land in 60% of your designation airport’s runway, as per FAR 121.195 for dry runway, or 115% for wet runway. FAR 121.195 are for dispatch only; if things change in flight, you can use 100% of runway if you have to. Note: AC 121.195 explains certification requirements for wet runways.
That is how it works most of the time, but there are times when things line up to cause problems. The book Fly the Wing lists some rule of thumbs that show differences from an ideal, dry runway:
Antiskid inoperative – add 75% from max antiskid breaking,
Ground spoiler inoperative – add 25%,
Reversers inoperative– add 10-20 %.
If you cross threshold at 100 feet instead of 50 – add 900 feet to touchdown distance.
1% increases in speed over correct V(ref) – add 2% change in landing roll.
1% increases from max landing weight - add 1% change in landing roll.
Add other factors like ATC, maintenance problems etc. that may be involved.
Most accident of this nature have several factors involved, both active and latent. There is usually no single cause. After an accident the media runs around trying to find “the cause” or someone to blame. Then they lose interest and move onto something else. It is when some of the factors above and others, line up, with no defences that accidents occur.
The following site is from Transport Canada’s site and shows that when landing on ice, the stopping distance can increase substantially without reversers as was discussed in previous post.
The following site has a calculator for the B737 landing distance.