BGP Update Source Logic, Bidirectional or Unidirectional?

Hello Community,

I have the above topology configured in BGP AS 200 as follows:

R2(config)#do show ip route rip | b Gateway
Gateway of last resort is not set

R     3.0.0.0/8 [120/1] via 10.1.234.3, 00:00:29, Ethernet0/0
R     4.0.0.0/8 [120/1] via 10.1.234.4, 00:00:14, Ethernet0/0

R2(config)#do show run | s router bgp
router bgp 200
 bgp router-id 2.2.2.2
 bgp log-neighbor-changes
 neighbor 3.3.3.3 remote-as 200
 neighbor 4.4.4.4 remote-as 200

R2(config)#do show ip bgp s | b Neighbor
Neighbor        V           AS MsgRcvd MsgSent   TblVer  InQ OutQ Up/Down  State/PfxRcd
3.3.3.3         4          200      25      26        3    0    0 00:19:16        2
4.4.4.4         4          200       0       0        1    0    0 never    Idle

R3(config)#do show ip route rip | b Gateway
Gateway of last resort is not set

R     2.0.0.0/8 [120/1] via 10.1.234.2, 00:00:06, Ethernet0/0
R     4.0.0.0/8 [120/1] via 10.1.234.4, 00:00:03, Ethernet0/0
     
R3(config)#do show run | s router bgp
router bgp 200
 bgp router-id 3.3.3.3
 bgp log-neighbor-changes
 neighbor 2.2.2.2 remote-as 200
 neighbor 2.2.2.2 update-source Loopback0
 neighbor 4.4.4.4 remote-as 200
 neighbor 4.4.4.4 update-source Loopback0

 
R3(config)#do show ip bgp s | b Neighbor
Neighbor        V           AS MsgRcvd MsgSent   TblVer  InQ OutQ Up/Down  State/PfxRcd
2.2.2.2         4          200      27      26        3    0    0 00:20:20        2
4.4.4.4         4          200      16      19        3    0    0 00:11:39        0

R4(config)#do show ip route rip | b Gateway
Gateway of last resort is not set

R     2.0.0.0/8 [120/1] via 10.1.234.2, 00:00:18, Ethernet0/0
R     3.0.0.0/8 [120/1] via 10.1.234.3, 00:00:09, Ethernet0/0
     
R4(config)#do show run | s router bgp
router bgp 200
 bgp router-id 4.4.4.4
 bgp log-neighbor-changes
 neighbor 2.2.2.2 remote-as 200
 neighbor 3.3.3.3 remote-as 200

R4(config)#do show ip bgp s | b Neighbor
Neighbor        V           AS MsgRcvd MsgSent   TblVer  InQ OutQ Up/Down  State/PfxRcd
2.2.2.2         4          200       0       0        1    0    0 never    Idle
3.3.3.3         4          200      21      18        3    0    0 00:13:39        2

If you pay attention, R3 has formed a neighbor relationship with R2 and R4 even though only R3 has the "update-source" command configured in the BGP process. I would have thought this command was needed on both sides in order for the neighbor relationship to form. Can someone explain? Thanks in advance