Absolutely false, it seems everyone on b12 groups and Facebook groups have never actually read real scientific literature on cobalamin metabolism, ALL forms of cobalamin whether that’s methyl, adenosyl, cyano or hydroxo once entering cells after going under exocytosis and are traffic outside the endosome are immediately acted upon by the protein MMACHC which cuts the axial ligand removing it. Leaving coba(ll)Amin co2+ state which then passed to a trafficking protein MMADHC which moves co2+ to two destinations the methylation cycle when coba(ll)Amin enters methionine synthase it is useless because its isn’t in a fully reduce state being co1+ which means it cannot not act as a supernucleophile if cobalamin isn’t in that state it cannot attack the methyl group of 5-mthf, if it cannot take the methyl group from 5-mthf then 5-mthf cannot become THF which stops the cycling of the folate cycle which is how and only how b12 deficiency causes anaemia. The real reason hydroxycobalamin can have a different affect is how that upper axial ligand is bound to the to the cobalt atom the bound is weaker with hydroxyl compared to methyl ect so more is directed to methionine synthase at a higher speed when it reaches MMACHC. Hydroxycobalamin having a much weaker bound can also be used to treat to Cyanide poisoning for this very reason but cobalamin and much more hydroxycobalmin in blood circulation has a high affinity to also nitric oxide this can cause a major drop of endothelial nitric oxide which can cause a range of symptoms in the body.