Yes it is true
This is said in Chapter 47 of Brahma Purana (on Archive by Dr. Narinder Sharma). It seems few Chapters are merged in this version on Archive. The equivalent Sanskrit Shlokas can be found in Chapter 50 of Brahma Purana (on sanskritdocuments).
The relavant Sanskrit shloka and it's English translation is as below:
ब्रह्मोवाच
श्रुत्वैतद् वचनं तस्य विश्वकर्मा सुकर्मकृत् ।
तत्क्षणात् कारयामास प्रतिमाः शुभलक्षणाः ॥ ५०.४८ ॥
Brahma said:
On hearing his (Vishnu's) words, Vishvakarma did all efficiently, instantaneously. He (Vishvakarma) made the idols of auspicious traits.
The summary of story can be found in this English abridged version.
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The story is slightly different in the local tradition. But there was no difference in Vishwakarma taking form of the sculptor and creating the Jagannath, Balarama and Subhadra idols. Accompanying Vishnu in the form of a brahmin is not mentioned. The local lore talks about sculptor asking absolutely undisturbed environment to make the idols - but after 14 days or so, Indradyumna gets anxious and knocks on the door. Upon being greeted by silence, he opens the door and sees no one inside - but only incomplete idols (no hands or feet).
And in terms of the explanations of the idol without hand and feet, I still adore the most beautiful narration given by Amish in his Ramachandra series novels. Had shared that image in twitter long ago. Still, goosebumps! :)