No this is absolutely not true. Marriages in secret are discouraged, and witnesses should be there in order to ensure that the rights of all parties are protected:
The Prophet (saws) said, "A virgin should not be married till she is
asked for her consent; and the matron should not be married till she
is asked whether she agrees to marry or not." It was asked, "O Allah's
Apostle! How will she (the virgin) express her consent?" He said, "By
keeping silent." Some people said, "If a virgin is not asked for her
consent and she is not married, and then a man, by playing a trick
presents two false witnesses that he has married her with her consent
and the judge confirms his marriage as a true one, and the husband
knows that the witnesses were false ones, then there is no harm for
him to consummate his marriage with her and the marriage is regarded
as valid." (Al-Bukhari 9:98)
Also, marriages are a public affair - they should be announced and celebrated:
The Prophet seeing a yellow mark (of perfume) on the clothes of
'Abdur-Rahman bin 'Auf, said, "What about you?" ' Abdur-Rahman
replied, "I have married a woman with a Mahr of gold equal to a
date-stone." The Prophet (saws) said, "May Allah bestow His Blessing
on you (in your marriage). Give a wedding banquet, (Walima) even with
one sheep." (Al-Bukhari 8:395)
These are the requirements:
- An agreement between the bride and groom to marry.
- Two sane witnesses
- A marriage gift to be paid by the groom to the bride either immediately, or deferred.
- A legal marriage contract.
- A guardian to represent the bride.
- Someone to officiate the marriage (usually the imam of a mosque, but any religious, pious person can do this).
- Walima (but this is post marriage, and can be held at any time).
And Allah Knows Best.