The root of the behavior lies in the sort order.
I've installed a new 1503 ASE with cp850 and a dictionary sort order and see the reported behavior.
Adaptive Server Enterprise/15.0.3/EBF 16381/P/Sun_svr4/OS 5.8/ase1503/2669/32-bit/FBO/Wed Nov 12 07:49:03 2008
if "Jones" like "%[QRS]%" print "yes" else print "no"
if "Jones" like "%[Q-S]%" print "yes" else print "no"
if "Jones" like "%[QRST]%" print "yes" else print "no"
if "Jones" like "%[Q-T]%" print "yes" else print "no"
go
no
no
no
yes
Looking at the output of sp_helpsort [particularly the part of the output that John unfortunately clipped out 
], I see this:
------------------------------------------------------------------
! " # $ % & ' ( ) * + , - . / : ; < = > ? @ [ \ ] ^ _ ` { | }
~ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
? 0 1 2 3 4 5 6 7 8 9 A a B b C
c D d E e F f G g H h I i
? J j K k L l M m N n O o P p Q q R r
S s T t U u V v W w X x Y y Z z
Now, consider the ranges "%[Q-S]%" and "%[Q-T]%". The difference is that the second one causes characters 's' and 'T' to be included in the range, and 's' is the last character in "Jones", so it matches.
In other words, under this dictionary sort order, [Q-T] is equivalent to [QqRrSsT] rather than [QRST].
1> if "Jones" like "%[Q-T]%" print "yes" else print "no"
2> if "Jonet" like "%[Q-T]%" print "yes" else print "no"
3> if "Jonet" like "%[Q-U]%" print "yes" else print "no"
4> go
yes
no
yes
-bret