Sam,
The story of Riegel or Rigel seems to have been a press invention, one among many. I have run across several versions even in fairly reputable magazines of the day - and some unlikely ones like "Good Housekeeping," of all places.
A bit of Titanic doggie trivia:
We've all heard stories (some apocrychal) of people who missed sailing on Titanic, but there was at least one pup who missed the boat of boats. Lady Duff Gordon's Pekingese Mr. Futze ("Footsie")always accompanied his mistress on trips but in April 1912 she reluctantly left him back at her Paris flat, looked after by her maid Rachel, because she was making only a quick business jaunt to NY and thought "Footsie" would have a better time "running about the garden or begging at the tea table."
One has few doubts, however, that had Footsie been aboard Titanic, he would surely have escaped on milady's lap, putting the number of occupants of the embattled emergency boat up to 13, an extra bit of bad luck the Duff Gordons surely did not need.
Randy