Steam should check if the partition/disk where .steam/steam/ resides has "exec" mount option.
External devices (and NTFS partitions) are usually mounted with noexec, so even if bin_steam.sh has +x, it can't be executed (and /usr/bin/steam tries to download again, install again and finally dies with an obscure error message).

I know it's a bit tricky, but something like:
grep df . | tail -n 1 | cut -d' ' -f 1 /etc/mtab | egrep '(user|users|noexec)'
should be a good starting point.