Anne, Thank you for caring for the PGM profile of Henry Tibbetts. We need all the help we can get cleaning-up and sourcing the profiles of these great New England ancestors.
I double checked Anderson this morning and he does say origins unknown. So per PGM the existing parents should be removed since the only supporting evidence is a single bp record. In cases like this we should go with Anderson pending further research.
However, in light of this being a rare name and the fact that you have found two children known to be siblings bp together suggests to me that you are really onto something novel (Anderson supports the idea that Remembrance was his sister p 40 GM). I would support the parents you propose. However, the evidence and any doubts should be stated clearly in the biography so that researchers know that this is not a set of parents that has been documented yet by Anderson or more recent research until now. It might spark further research such as a probate record search.
My only pause is that he was a passenger on the James in 1635 and almost all of those passengers were from South England mostly from Salisbury, Wiltshire, Hampton, and Langford, Oxfordshire or they were from London. Moreover, his wife's family, the Austins were also from Hampshire.