No, they're wrong actually if you look at the different translations and the Latin and Greek words behind the word rapture'.

The word 'rapture' is not listed in the English bible. But it is listed in the Latin Vulgate bible, written by Jerome in the early 400's AD. The word there is ‘rapiemur‘, 'raeptius' or 'rapturo' , which translated into English means 'rapture'. It is found here in the English bible:

1 Thessalonians 4:17
17 Then we which are alive and remain shall be *caught up* together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord.

In English bibles, ‘rapiemur‘, 'raeptius' or 'rapturo' is transliterated into 'caught up'. That happens sometimes during the translation process to try to communicate the point more familiarly.

The original Thessalonian manuscripts however were written in Greek. There were actually no 'English' words at all in the original bibles, including the word 'bible' itself. And the original Greek word for 'rapture' is listed in English script as 'harpazo', which means 'to rapture up into the air', or to 'snatch away'.

It was this original Greek term 'harpazo' that Jerome later translated into Latin as ‘rapiemur‘, 'raptus' or 'raeptius', which was later translated into English as 'rapture'. These terms all mean the same thing: 'to be caught up'.

[link to en.wikipedia.org (secure)]
[link to www.raptureready.com (secure)]

So the rapture is very much a written part of the bible. The only thing being contested is the timing of the rapture.