That's the excuse often said by Nintendo fanboys in order to antagonize Rare and damage control the selling to Microsoft but that's silly. Rare may had some layoffs, but still it was perhaps the strongest western dev they had a the time. It was actually Microsoft's blame and their inability to properly manage Rare and it's franchises that ruined it. At Nintendo hands, it's very likely they could still keep the relevance they had. Remember, Retro also had lay offs, most of the Prime series departed, but Nintendo still managed to keep it strong and able to develop two great DK games. Rare probably would have made a sequel to DK 64 for GCN that would be a major seller, as well it's other big IPs, strongly identified to Nintendo's ecosystem and audience. Rare's IPs never managed to have the same appealing and reception from MS's crowd.
Giving away strong and highly appealing to the western crowd IPs, such as Killer Instinct, Perfect Dark, Conker, Banjo, etc.. took a hit into Nintendo's range diversity and it's appeal toward the western audience was severely held back. Nintendo never managed to create something close to Rare's aesthetics to properly fill the void left. There's nothing on Nintendo's library closely resembling aesthetics from Rare games such as KI, PD and Conker. This diversity was lost with Rare's sellout and consequently the lost of it's IPs. That was a very short-sighted decision from Nintendo, not only because they lost strong, western appealing IPs, but they chose to give them to it's competitor. The "Rare was on a downward spiral" excuse doesn't make any sense either. Rare developed, from 2000-2002, one of the best N64 titles such as Banjo Tooie, Perfect Dark and Conker's Bad Fur Day. Star Fox Adventures is regarded as a failure, but it's obvious incomplete and the sellout negotiations took a hit in the final product, not because Rare was "falling apart" as some claim.
Imagine if Sony sells Naughty Dog along with Uncharted and Last of Us for Nintendo? It would be a similar situation.
That's the reason why there's expectations among Nintendo fans for Retro and NLG to properly fill the void left from Rare (and others ex-secord-parties). There's very few Nintendo IP's at the moment targeting the west especifically, something they had in the past.