Hello Judi -
I think the error re: William being the son of Thomas and Phoebe is widespread. It's simply the only entry on the IGI which "fits" - and as Beds is so well covered on the IGI, it is assumed to be correct.
There is no incontrovertible proof that William b 1792-ish is the son of John and Sarah Armstrong of Ravensden, because there appears to be no baptism. But the circumstantial evidence is almost overwhelming. Plus, of course, the fact that William of Upper Gravenhurst probably died in 1807.
The link backwards is also circumstantial: John Armstrong who died in 1826 in Ravensden aged 66 is likely to have been John Armstrong baptised in 1761 in Wilstead, son of John Armstrong and Edith Grange. John and Edith were both buried in Maulden by 1773, and the apprenticeship of their son William by the Maulden Overseers in 1766 indicates that they were poor, and possibly a charge on the parish. How John got from Maulden to Ravensden is unknown, but he too could have been apprenticed or otherwise placed out by the Maulden overseers.
A new piece of linking evidence emerged just yesterday. A Sarah Armstrong was baptised in Maulden in 1766, daughter of John and Mary. I have no idea who John and Mary were - yet. I can't find a likely marriage for a John Armstrong and a Mary. The NBI doesn't turn up any unaccounted for Johns who could have been Sarah's father, other than John who was married to Edith! Did John perhaps have and acknowledge a child outside his marriage? We know he was in Maulden in 1766 because of William's apprenticeship.....
The only Sarah buried in Beds on the National Burial Index that isn't otherwise accounted for is Sarah buried in Ravensden in 1813 aged 47 - so born 1766 - a perfect match.
So the possibility is that John married (or perhaps didn't marry? if John Snr DID stray, then John and Sarah were half-brother and sister!) Sarah of Maulden, and they made their way to Ravensden before 1787 when their first child was baptised there. .
Fortunately the line back from John and Edith to the original John and Sarah born about 1670-1680 is fairly well documented, as are the links downwards from the Ravensden and Thurleigh families.
You and I are linked because your William 1792 and my John 1802 were almost certainly brothers - sons of John Armstrong and Sarah in Ravensden.
Re: UK research - virtually everything you need is available online nowadays. The IGI covers Beds reasonably well, as David has outlined in an earlier post. But you need to watch out for member entries, which can be very misleading, ad they are great ones for extrapolating birth dates and places backwards from marriage entries!
Ancestry covers the census information from 1841 to 1901 and has a lot of other useful information, including the Wilstead parish records in their Parish and Probate database. FreeBMD is now virtually complete from 1837 to about 1912 and is excellent for locating certificates. FreeREG is also coming along, but you need to be lucky, as it is still in the very early stages. Family History Online is a pay-per-view database which has Bedfordshire well covered on the NBI, though virtually no other Beds information. Genes Reunited, as you have already found, is valuable - though you need to be prepared for other people's errors - I once had a whole fictitious branch in my tree, because I confused two people with the same name from the same village! It took three of us almost a year to sort it all out....
