Well, when it is the 18th guy that day that claims to have lounge access based on something he shows on his phone, LH's position is facilitated enormously when said display shows "physical card needed to access this lounge". Additionally, the requirement that the agent was enforcing is written down in their access rules.

It would help if UA changes that line to "this virtual card is a valid *A lounge access credential", along with "Lounge agent: verify access using UAMP #XXXXXXXX ".

Dedicated topic: https://www.flyertalk.com/forum/united-airlines-mileageplus/1953295-recent-denials-admission-lounges-due-lack-ua-g-card-2019-2020-a.html