I love Janet Lansbury, and I say that as someone who is a firm believer in the fourth trimester, safe bed sharing, etc.
This woman thinks it's ok for a baby to cry if they're held
Yes... What she actually says is once all other reasons have been ruled out consider that your child may feel overwhelmed or frustrated or any number of nebulous emotions that they can't express. So, rather than feeling useless as a parent because you haven't "fixed" it, and rather than leaving them to cry it out, you just be emotionally present and support your child while they let it out.
In my experience, her critics have rarely read our understood her work. I'd highly recommend listening to her podcast. It all makes much more sense when you hear her tone of voice.
With regards to playing on their own, at four months, that may only be for a few minutes. Or even less if they aren't used to it. But how often have you seen a child looking at something only to have a well meaning adult thrust a toy in their face? Her point is that you respect them and the things that interest them. If they aren't asking to be entertained, don't jump in there. And, if they are, maybe just take it slowly to see what interests them, rather than rushing in all singing and dancing.
The point of RIE parenting is that it's respectful to both the baby and the parent. Sorry, I'm probably waffling but I'm both sleep deprived and excitable. Not a coherent mix...