Although i dont own monitors my fellow herpers who i see every weekend do. also i own tegus, which are the new world version of monitors. so that bieng said here is my opinion:
Monitors can be "tamed" to some degree but the term is vey overused as this is not usuall.
i know and see 8 people with monitors every weekend all of them are called "tame" but only two of them really tame as skiploder said the real "tame" ones need heat. the two people who really have tame monitors give them 4 basking spots throughout theere house. however it has taken them 6 years for them to actually not see them as a threat. This is the same with tegus.
for example when i was twelve i got my first tegus. they were columbian golden and when i bought them at an expo they were cold and seemed very friendly. after leavin them in there enclosure for about three hours when i opened the up to check on them they jumped up bit my fingers and made me bleed. so yes monitors can be "tame but it takes time for them to get used to you.

Hope this helps,
Jeremy browning
7.8.0 corn snakes ( anery anery motley normal bloodred motley snow amber striped amelanistic )
0.1.0 pastel ball python
1.0.0 bearded dragon
2.2.0 mexican rosy boas
1.1.0 redtail boaconstrictors (normal and hypo both het for cyclone )
3.3.0 orange eyed crocadile skinks
4.2.0 red eyed tree frogs
1.1.0 golden tegus
1.1.0 giant leaf-tailed geckos
1.1.0 satanic leaf-tailed geckos
1.1.0 mossy leaf-tailed geckos
1.1.0 giant day geckos
3.7.12 crested geckos ( harley red harley and green flame tin )
4.10.0 gargoyle geckos ( striped and reticulated )
45.45.8 dart frogs ( tinctorius (cobalt, regina, green sip, powder blue and alanis) auratus ( mint and costa rican ) azureus, leucameleas ( bumblebees ), Dendrobates ventrimaculatus (thumbnail) and many other kinds. )


" the people from PETA are no more qualified to talk about reptile ethics than sarah palin is to lead the free world"