MPLS and EIGRP, going the Distance, (Admin Distance).

Can you solve this puzzle?
R2, R3 and R4 create the service provider network, with MPLS on all three routers, and iBGP at the PE routers.  R1 and R5 are the CE routers.
R2, prefers the BGP next hop of 4.4.4.4 for network 5.5.5.5 (R5 loopback). R4, at 4.4.4.4 is an iBGP neighbor.

R2#show ip route vrf v | inc 5.5.5.0
B       5.5.5.0 [200/409600] via 4.4.4.4, 00:06:47

Is R2 preferring an iBGP learned route, which has an AD of 200, over a EIGRP route, which would have an AD of 90?
Can you identify why the routing for 5.5.5.0 on the VRF of R2 is using BGP instead of EIGRP?

Below are the relevant portions of the configuration, which also can serve as a great review of how to configure MPLS VPNs.
R1, CE router:

R1#show run
interface Loopback0
 ip address 1.1.1.1 255.255.255.0
!
interface FastEthernet0/0
 ip address 10.1.12.1 255.255.255.0
 duplex auto
 speed auto
!
interface Serial0/0
 ip address 10.1.215.1 255.255.255.0
!

router eigrp 1
 network 0.0.0.0
 no auto-summary

R2, PE Router:

R2#show run
!
ip vrf v
 rd 1:1
 route-target export 1:1
 route-target import 1:1
!
!
interface Loopback0
 ip address 2.2.2.2 255.255.255.255
 ip ospf 1 area 0
!
interface FastEthernet0/0
 ip vrf forwarding v
 ip address 10.1.12.2 255.255.255.0
!
interface FastEthernet0/1
 ip address 10.1.23.2 255.255.255.0
 ip ospf 1 area 0
 mpls ip
!
router eigrp 1
 no auto-summary
 !
 address-family ipv4 vrf v
  redistribute bgp 234 metric 1 10000 1 1 1
  network 10.1.12.2 0.0.0.0
  auto-summary
  autonomous-system 1
 exit-address-family
!
router ospf 1
 log-adjacency-changes
!
router bgp 234
 no bgp default ipv4-unicast
 bgp log-neighbor-changes
 neighbor 4.4.4.4 remote-as 234
 neighbor 4.4.4.4 update-source Loopback0
 !
 address-family vpnv4
  neighbor 4.4.4.4 activate
  neighbor 4.4.4.4 send-community extended
 exit-address-family
 !
 address-family ipv4 vrf v
  redistribute eigrp 1
  no synchronization
 exit-address-family
!
ip forward-protocol nd
!

R3, P router:

R3#show run

interface Loopback0
 ip address 3.3.3.3 255.255.255.255
!
interface FastEthernet0/0
 ip address 10.1.34.3 255.255.255.0
 mpls ip
!
interface FastEthernet0/1
 ip address 10.1.23.3 255.255.255.0
 mpls ip
!
router ospf 1
 log-adjacency-changes
 network 0.0.0.0 255.255.255.255 area 0
!

R4: PE Router

R4#show run
!
ip vrf v
 rd 1:1
 route-target export 1:1
 route-target import 1:1
!
!
interface Loopback0
 ip address 4.4.4.4 255.255.255.255
 ip ospf 1 area 0
!
interface FastEthernet0/0
 ip address 10.1.34.4 255.255.255.0
 ip ospf 1 area 0
 mpls ip
!
interface FastEthernet0/1
 ip vrf forwarding v
 ip address 10.1.45.4 255.255.255.0
!
router eigrp 1
 no auto-summary
 !
 address-family ipv4 vrf v
  redistribute bgp 234 metric 1 1 1 1 1
  network 10.1.45.4 0.0.0.0
  auto-summary
  autonomous-system 1
 exit-address-family
!
router ospf 1
 log-adjacency-changes
!
router bgp 234
 no bgp default ipv4-unicast
 bgp log-neighbor-changes
 neighbor 2.2.2.2 remote-as 234
 neighbor 2.2.2.2 update-source Loopback0
 !
 address-family vpnv4
  neighbor 2.2.2.2 activate
  neighbor 2.2.2.2 send-community extended
 exit-address-family
 !
 address-family ipv4 vrf v
  redistribute eigrp 1
  no synchronization
 exit-address-family

R5: CE Router

R5#show run
!
interface Loopback0
 ip address 5.5.5.5 255.255.255.0
!
interface Serial0/0
 ip address 10.1.215.5 255.255.255.0
 clock rate 64000
!
interface FastEthernet0/1
 ip address 10.1.45.5 255.255.255.0
!
router eigrp 1
 network 0.0.0.0
 no auto-summary
!

Now for a couple show commands on R1:

R1#show ip route eigrp
     5.0.0.0/24 is subnetted, 1 subnets
D       5.5.5.0 [90/435200] via 10.1.12.2, 00:19:08, FastEthernet0/0
     10.0.0.0/24 is subnetted, 3 subnets
D       10.1.45.0 [90/307200] via 10.1.12.2, 00:19:08, FastEthernet0/0
R1#

R1#show ip eigrp topology
IP-EIGRP Topology Table for AS(1)/ID(10.1.215.1)

Codes: P - Passive, A - Active, U - Update, Q - Query, R - Reply,
       r - reply Status, s - sia Status

P 1.1.1.0/24, 1 successors, FD is 128256
        via Connected, Loopback0
P 5.5.5.0/24, 1 successors, FD is 435200
        via 10.1.12.2 (435200/409600), FastEthernet0/0
        via 10.1.215.5 (2297856/128256), Serial0/0
P 10.1.12.0/24, 1 successors, FD is 281600
        via Connected, FastEthernet0/0
P 10.1.45.0/24, 1 successors, FD is 307200
        via 10.1.12.2 (307200/281600), FastEthernet0/0
        via 10.1.215.5 (2195456/281600), Serial0/0
P 10.1.215.0/24, 1 successors, FD is 2169856
        via Connected, Serial0/0
R1#

And some on R2, the PE router:

R2#show ip route vrf v

Routing Table: v
Codes: C - connected, S - static, R - RIP, M - mobile, B - BGP
       D - EIGRP, EX - EIGRP external, O - OSPF, IA - OSPF inter area
       N1 - OSPF NSSA external type 1, N2 - OSPF NSSA external type 2
       E1 - OSPF external type 1, E2 - OSPF external type 2
       i - IS-IS, su - IS-IS summary, L1 - IS-IS level-1, L2 - IS-IS level-2
       ia - IS-IS inter area, * - candidate default, U - per-user static route
       o - ODR, P - periodic downloaded static route

Gateway of last resort is not set

     1.0.0.0/24 is subnetted, 1 subnets
D       1.1.1.0 [90/409600] via 10.1.12.1, 00:31:48, FastEthernet0/0
     5.0.0.0/24 is subnetted, 1 subnets
B       5.5.5.0 [200/409600] via 4.4.4.4, 00:02:34
     10.0.0.0/24 is subnetted, 3 subnets
C       10.1.12.0 is directly connected, FastEthernet0/0
B       10.1.45.0 [200/0] via 4.4.4.4, 00:31:48
D       10.1.215.0 [90/2195456] via 10.1.12.1, 00:31:21, FastEthernet0/0

R2#show ip eigrp vrf v topology
IP-EIGRP Topology Table for AS(1)/ID(10.1.12.2) Routing Table: v

Codes: P - Passive, A - Active, U - Update, Q - Query, R - Reply,
       r - reply Status, s - sia Status

P 1.1.1.0/24, 1 successors, FD is 409600
        via 10.1.12.1 (409600/128256), FastEthernet0/0
P 5.5.5.0/24, 1 successors, FD is 409600
        via VPNv4 Sourced (409600/0)
P 10.1.12.0/24, 1 successors, FD is 281600
        via Connected, FastEthernet0/0
P 10.1.45.0/24, 1 successors, FD is 281600
        via VPNv4 Sourced (281600/0)
P 10.1.215.0/24, 1 successors, FD is 2195456
        via 10.1.12.1 (2195456/2169856), FastEthernet0/0
R2#