What you propose is fine - you'll get the Silver perks as long as a Silver member is on the booking. Doesn't have to be the person paying.
ETA: Just to give a link to the BA language on this:
https://www.britishairways.com/en-gb...ilver-benefits
You can see that the relevant text is "
You must be travelling on the booking for the benefit to apply", as long as they are travelling, that's all you need. No mention of having to be the one who made the booking or paid for it.