How? Budapest Memorandum only required parties to respect borders, not to defend them. They only need to "seek immediate United Nations Security Council action to provide assistance" when there is threat of using nuclear weapons.
Putin's claim is that he signed it with the legitimate government of Ukraine and that Ukraine is no longer legitimately governed since the Maidan "coup".
It's similar in nature to the UK's insistence that Venezuelan gold cant be sent back to Venezuela - since it is not legitimately governed. Or when revolutions take place and new governments decide that the debts of the "old" government dont apply to the new.
US also threatened sanctions against Ukraine in 2004 in violation of article 3, presumably under the same theory (& because they just didnt like yanukovych).
International law is mostly a matter might makes right and/or opinion it seems. There is no court, after all. One side's coup is another's spontaneous democratic uprising and one side's free and fair elections is another party's rigged ballot.
UK has not seized Venezuelan gold - as soon as Venezuela will get recognized government, UK will restore Venezuelan rights to their gold.
How this even compares to Crimea? Russia has no intention to give Crimea back - no matter what government is in Ukraine. Russia was already very nervous about Sevastopol naval base under Yanukovich, when the rent agreement was running out and that is the only reason for seizing Crimea, as this allows it to maintain than naval base. It is also a theft, as so far Russia was paying rent for that base and now it doesn't have to.
Ask Venezuelans what should happen to the gold and majority would say give it back. Access was cut off precisely when they needed funds the most.
Crimea won't be given back, no. They ran a vote and asked the majority ~85% ethnic Russian Crimeans which country they'd like to belong to and, after maidan, the outcome was a forgone conclusion with or without the boycotts.
Ukraine and western powers tellingly opted to argue that the vote was wrong because it was in violation of Ukraine's constitution rather than it didnt reflect the will of those voting.
Even if Western powers didnt routinely flout international law when it suited them (e.g. supporting Israeli settlements on stolen land), it's a little bit awkward to declare a democratic vote illegal if you're trying to position yourself as the world's #1 fan of democracy.
Ironically if America could have held itself to higher ethical standards in the last two decades it would probably be in a better position to push Russia's new expansion back.